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Yu Zhang

Publications and source records attributed to Yu Zhang.

At least 1,711 records · Page 95Linked to original sources
arXiv2008

On the concentration and the convergence rate with a moment condition in first passage percolation

We consider the first passage percolation model on the ${\bf Z}^d$ lattice. In this model, we assign independently to each edge $e$ a non-negative passage time $t(e)$ with a common distribution $F$. Let $a_{0,n}$ be the passage time from the origin to $(n,0,..., 0)$. Under the exponential tail assumption, Kesten (1993) and Talagrand (1995) investigated the concentration of $a_{0,n}$ from its mean using different methods. With this concentration and the exponential tail assumption, Alexander gave an estimate for the convergence rate for ${\bf E} a_{0,n}$. In this paper, focusing on a moment condition, we reinvestigate the concentration and the convergence rate for $a_{0,n}$ using a special martingale structure.

math.PR↗
arXiv2008

Stellar and Dust Properties of Local Elliptical Galaxies: Clues to the Onset of Nuclear Activity

We study the stellar and dust properties of a well-defined sample of local elliptical galaxies to investigate the relationship between host galaxy properties and nuclear activity. We select a complete sample of 45 ellipticals from the Palomar spectroscopic survey of nearby galaxies, which includes 20 low-luminosity active galactic nuclei classified as LINERs and 25 inactive galaxies. Using a stellar population synthesis method, we compare the derived stellar population properties of the LINER versus the inactive subsamples. We also study the dust and stellar surface brightness distributions of the central regions of these galaxies using high-resolution images obtained with the {\it Hubble Space Telescope}. Relative to the inactive subsample, ellipticals hosting LINERs share similar total optical and near-infrared luminosity, central stellar velocity dispersions, and nuclear stellar populations as judged from their luminosity-weighted ages and metallicities. LINERs, on the other hand, have a larger fraction of core-type central surface brightness profiles and a much higher frequency of circumnuclear dust structures. Our results support the suggestion that LINERs are powered by low-luminosity AGNs rather than by young or intermediate-age stars. Nuclear activity in nearby elliptical galaxies seems to occur preferentially in those systems where sufficient cold interstellar material has managed to accumulate, perhaps via cooling condensations from hot gas.

astro-ph↗
arXiv2008

The time constant vanishes only on the percolation cone in directed first passage percolation

We consider the directed first passage percolation model on ${\bf Z}^2$. In this model, we assign independently to each edge $e$ a passage time $t(e)$ with a common distribution $F$. We denote by $\vec{T}({\bf 0}, (r,θ))$ the passage time from the origin to $(r, θ)$ by a northeast path for $(r, θ)\in {\bf R}^+\times [0,π/2]$. It is known that $\vec{T}({\bf 0}, (r, θ))/r$ converges to a time constant $\vecμ_F (θ)$. Let $\vec{p}_c$ denote the critical probability for oriented percolation. In this paper, we show that the time constant has a phase transition divided by $\vec{p}_c$, as follows: (1) If $F(0) < \vec{p}_c$, then $\vecμ_F(θ) >0$ for all $0\leq θ\leq π/2$. (2) If $F(0) = \vec{p}_c$, then $\vecμ_F(θ) >0$ if and only if $θ\neq π/4$. (3) If $F(0)=p > \vec{p}_c$, then there exists a percolation cone between $θ_p^-$ and $θ_p^+$ for $0\leq θ^-_p< θ^+_p \leq π/2$ such that $\vecμ (θ) >0$ if and only if $θ\not\in [θ_p^-, θ^+_p]$. Furthermore, all the moments of $\vec{T}({\bf 0}, (r, θ))$ converge whenever $θ\in [θ_p^-, θ^+_p]$. As applications, we describe the shape of the directed growth model on the distribution of $F$. We give a phase transition for the shape divided by $\vec{p}_c$.

math.PR↗
arXiv2008

Shape fluctuations are different in different directions

We consider the first passage percolation model on $\mathbf{Z}^2$. In this model, we assign independently to each edge $e$ a passage time $t(e)$ with a common distribution $F$. Let $T(u,v)$ be the passage time from $u$ to $v$. In this paper, we show that, whenever $F(0) 0$ and $F(r)>\vec{p}_c$, it is known that there exists $M$ such that for all $n$, $σ^2(T((0,0),(n,n)))\leq M$. These results tell us that shape fluctuations not only depend on distribution $F$, but also on direction. When showing this result, we find the following interesting geometrical property. With the special distribution above, any long piece with $r$-edges in an optimal path from $(0,0)$ to $(n,0)$ has to be very circuitous.

math.PR↗
arXiv2007

Dirac quasinormal modes of a Schwarzschild black hole surrounded by free static spherically symmetric quintessence

We evaluate the quasinormal modes of massless Dirac perturbation in a Schwarzschild black hole surrounded by the free static spherically symmetric quintessence by using the third-order WKB approximation. The result shows that due to the presence of quintessence, the massless field damps more slowly. The real part of the quasinormal modes increases and the the absolute value of the imaginary part increases when the state parameter $w_q$ increases. In other words, the massless Dirac field decays more rapidly for the larger $w_q$. And the peak value of potential barrier gets higher as $|k|$ increases and the location of peak moves along the right for fixed $w_q$.

gr-qc↗
arXiv2007

Quasinormal modes of a Schwarzschild black hole surrounded by free static spherically symmetric quintessence: Electromagnetic perturbations

In this paper, we evaluated the quasinormal modes of electromagnetic perturbation in a Schwarzschild black hole surrounded by the static spherically symmetric quintessence by using the third-order WKB approximation when the quintessential state parameter $ w_{q}$ in the range of $-1/3<w_{q}<0$. Due to the presence of quintessence, Maxwell field damps more slowly. And when at $-1<w_{q}<-1/3$, it is similar to the black hole solution in the ds/Ads spacetime. The appropriate boundary conditions need to be modified.

gr-qc↗
arXiv2007

Shape curvatures and transversal fluctuations in the first passage percolation model

We consider the first passage percolation model on the square lattice. In this model, $\{t(e): e{an edge of}{\bf Z}^2 \}$ is an independent identically distributed family with a common distribution $F$. We denote by $T({\bf 0}, v)$ the passage time from the origin to $v$ for $v\in {\bf R}^2$ and $B(t)=\{v\in {\bf R}^d: T({\bf 0}, v)\leq t\}.$ It is well known that if $F(0) < p_c$, there exists a compact shape ${\bf B}_F\subset {\bf R}^2$ such that for all $ε>0$, $t {\bf B}_F(1-ε) \subset {B(t)} \subset t{\bf B}_F(1+ε)$, eventually with a probability 1. For each shape boundary point $u$, we denote its right- and left-curvature exponents by $κ^+(u)$ and $κ^-(u)$. In addition, for each vector $u$, we denote the transversal fluctuation exponent by $ξ(u)$. In this paper, we can show that $ξ(u) \leq 1-\max\{κ^-(u)/2, κ^+(u)/2\}$ for all shape boundary points $u$. To pursue a curvature on ${\bf B}_F$, we consider passage times with a special distribution infsupp$(F)=l$ and $F(l)=p > \vec{p}_c$, where $l$ is a positive number and $\vec{p}_c$ is a critical point for the oriented percolation model. With this distribution, it is known that there is a flat segment on the shape boundary between angles $0< θ_p^- < θ_p^+< 90^\circ$. In this paper, we show that the shape are strictly convex at the directions $θ_p^\pm$. Moreover, we also show that for all $r>0$, $ξ((r, θ^\pm_p)) = 0.5$ and $ξ((r, θ)) =1$ for all $θ_p^- <θ< θ_p^+$ and $r>0$.

math.PR↗
arXiv2006

On Completeness of Logical Relations for Monadic Types

Software security can be ensured by specifying and verifying security properties of software using formal methods with strong theoretical bases. In particular, programs can be modeled in the framework of lambda-calculi, and interesting properties can be expressed formally by contextual equivalence (a.k.a. observational equivalence). Furthermore, imperative features, which exist in most real-life software, can be nicely expressed in the so-called computational lambda-calculus. Contextual equivalence is difficult to prove directly, but we can often use logical relations as a tool to establish it in lambda-calculi. We have already defined logical relations for the computational lambda-calculus in previous work. We devote this paper to the study of their completeness w.r.t. contextual equivalence in the computational lambda-calculus.

cs.LO↗
arXiv2006

Collective Shape-Phases of Interacting Fermion Systems

A microscopic theory is presented for identifying shape-phase structures and transitions in interacting fermion systems. The method provides a microscopic description for collective shape-phases, and reveals detailed dependence of such shape-phases on microscopic interaction strengths. The theory is generally applicable to fermion systems such as nuclei, quarks, and in particular trapped cold atoms, where shape-phases may be observed and investigated in a controlled manner.

nucl-th↗
arXiv2006

Singularity points for first passage percolation

Let $0<a<b<\infty$ be fixed scalars. Assign independently to each edge in the lattice $\mathbb{Z}^2$ the value $a$ with probability $p$ or the value $b$ with probability $1-p$. For all $u,v\in\mathbb{Z}^2$, let $T(u,v)$ denote the first passage time between $u$ and $v$. We show that there are points $x\in\mathbb{R}^2$ such that the ``time constant'' in the direction of $x$, namely, $\lim_{n\to\infty}n^{-1}\mathbf{E}_p[T(\mathbf{0},nx)],$ is not a three times differentiable function of $p$.

math.PR↗
arXiv2006

A Geometrical Structure for an Infinite Oriented Cluster and its Uniqueness

We consider the supercritical oriented percolation model. Let ${\fK}$ be all the percolation points. For each $u\in {\fK}$, we write $γ_u$ as its right-most path. Let $G=\cup_u γ_u$. In this paper, we show that $G$ is a single tree with only one topological end. We also present a relationship between ${\fK}$ and $G$ and construct a bijection between ${\fK}$ and $\Z$ using the preorder traversal algorithm. Through applications of this fundamental graph property, we show the uniqueness of an infinite oriented cluster by ignoring finite vertices.

math.PR↗
arXiv2005

The distribution of the minimum height among pivotal sites in critical two-dimensional percolation

Let L_n denote the lowest crossing of the 2n \times 2n square box B(n) centered at the origin for critical site percolation on Z^2 or critical site percolation on the triangular lattice imbedded in Z^2, and denote by Q_n the set of pivotal sites along this crossing. On the event that a pivotal site exists, denote the minimum height that a pivotal site attains above the bottom of B(n) by M_n:= min{m:(x,-n+m)\in Q_n for some -n\le x\le n}. Else, define M_n = 2n. We prove that P(M_n < m) \asymp m/n, uniformly for 1\le m\le n. This relation extends Theorem 1 of van den Berg and Jarai (2003) who handle the corresponding distribution for the lowest crossing in a slightly different context. As a corollary we establish the asymptotic distribution of the minimum height of the set of cut points of a certain chordal SLE_6 in the unit square of C.

math.PR↗
arXiv2005

Quantum Phase Transitions in the U(5)-O(6) Large N limit

The U(5)-O(6) transitional behavior of the Interacting Boson Model in the large N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B(E2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviors of these quantities are greatly enhanced with increasing of the total number of bosons N, especially fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n_d in the first excited 0^+ state and the ground state, and another quantity related to the isomer shift behave similarly in both the O(6)-U(5) large N and U(5)-SU(3) phase transitions.

nucl-th↗
arXiv2005

The divergence of fluctuations for the shape on first passage percolation

Consider the first passage percolation model on ${\bf Z}^d$ for $d\geq 2$. In this model we assign independently to each edge the value zero with probability $p$ and the value one with probability $1-p$. We denote by $T({\bf 0}, v)$ the passage time from the origin to $v$ for $v\in {\bf R}^d$ and $$B(t)=\{v\in {\bf R}^d: T({\bf 0}, v)\leq t\}{and} G(t)=\{v\in {\bf R}^d: ET({\bf 0}, v)\leq t\}.$$ It is well known that if $p < p_c$, there exists a compact shape $B_d\subset {\bf R}^d$ such that for all $ε>0$ $$t B_d(1-ε) \subset {B(t)} \subset tB_d(1+ε){and} G(t)(1-ε) \subset {B(t)} \subset G(t)(1+ε) {eventually w.p.1.}$$ We denote the fluctuations of $B(t)$ from $tB_d$ and $G(t)$ by &&F(B(t), tB_d)=\inf \{l:tB_d(1-{l\over t})\subset B(t)\subset tB_d(1+{l\over t})\} && F(B(t), G(t))=\inf\{l:G(t)(1-{l\over t})\subset B(t)\subset G(t)(1+{l\over t})\}. The means of the fluctuations $E[F(B(t), tB_d]$ and $E[F(B(t), G(t))]$ have been conjectured ranging from divergence to non-divergence for large $d\geq 2$ by physicists. In this paper, we show that for all $d\geq 2$ with a high probability, the fluctuations $F(B(t), G(t))$ and $F(B(t), tB_d)$ diverge with a rate of at least $C \log t$ for some constant $C$. The proof of this argument depends on the linearity between the number of pivotal edges of all minimizing paths and the paths themselves. This linearity is also independently interesting.

math.PR↗
arXiv1997

The Statistics of Density Peaks and the Column Density Distribution of the Lyman-Alpha Forest

We develop a method to calculate the column density distribution of the Lyman-alpha forest for column densities in the range $10^{12.5} - 10^{14.5} cm^{-2}$. The Zel'dovich approximation, with appropriate smoothing, is used to compute the density and peculiar velocity fields. The effect of the latter on absorption profiles is discussed and it is shown to have little effect on the column density distribution. An approximation is introduced in which the column density distribution is related to a statistic of density peaks (involving its height and first and second derivatives along the line of sight) in real space. We show that the slope of the column density distribution is determined by the temperature-density relation as well as the power spectrum on scales $2 h Mpc^{-1} < k < 20 h Mpc^{-1}$. An expression relating the three is given. We find very good agreement between the column density distribution obtained by applying the Voigt-profile-fitting technique to the output of a full hydrodynamic simulation and that obtained using our approximate method for a test model. This formalism then is applied to study a group of CDM as well as CHDM models. We show that the amplitude of the column density distribution depends on the combination of parameters $(Ω_b h^2)^2 T_0^{-0.7} J_{HI}^{-1}$, which is not well-constrained by independent observations. The slope of the distribution, on the other hand, can be used to distinguish between different models: those with a smaller amplitude and a steeper slope of the power spectrum on small scales give rise to steeper distributions, for the range of column densities we study. Comparison with high resolution Keck data is made.

astro-ph↗
arXiv1997

Physical Properties of the Lyman Alpha Forest in a Cold Dark Matter Cosmology

We discuss the origin and physical nature of the Lya forest absorption systems as found in hydrodynamical simulations of the Intergalactic Medium in a standard Cold Dark Matter cosmology (Omega=1, H0=50 km/s/Mpc, sigma_8=0.7). The structures of the systems that give rise to the Lya forest span a wide range in morphologies, depending on the density contrast. The absorption properties of the forest clouds correlate strongly with those of the underlying physical systems from which they arise. The highest column density systems (log N_HI > 15), correspond to highly overdense spheroidal structures, moderate column density systems (13 < log N_HI < 14), correspond to filaments, and the lowest density absorption systems originate from discrete fluctuations within underdense regions a few megaparsecs across, cosmic minivoids. Most of the intergalactic HeII opacity arises from these underdense regions. We are able to account for the distribution of optical depths in our synthesized spectra entirely by absorption due to discrete systems. We find that virtually all the baryons in the simulation fragment into structures that we can identify with discrete absorption lines, with at most 5% remaining in a smoothly distributed component (the Gunn-Peterson effect). We compare our results with the cloud ionization parameters inferred from Keck HIRES measurements of carbon and silicon in the Lya forest. Combining with constraints imposed by measurements of the mean intergalactic HI opacity, we find 0.03 < Omega_b < 0.08 and 0.3 < (Gamma_HI/ 10^-12 s^-1) < 1 at z=3-3.5.

astro-ph↗
arXiv1997

First Structure Formation: I. Primordial Star Forming Regions in hierarchical models

We investigate the possibility of very early formation of primordial star clusters from high-σperturbations in cold dark matter dominated structure formation scenarios. For this we have developed a powerful 2-level hierarchical cosmological code with a realistic and robust treatment of multi-species primordial gas chemistry, paying special attention to the formation and destruction of hydrogen molecules, non-equilibrium ionization, and cooling processes. We performed 3-D simulations at small scales and at high redshifts and find that, analogous to simulations of large scale structure, a complex system of filaments, sheets, and spherical knots at the intersections of filaments form. On the mass scales covered by our simulations (5x10^5 - 1x10^9\Ms) that collapse at redshifts z>25, we find that only at the spherical knots can enough H2 be formed (n_{H_2}/n_H > 5x10^-4) to cool the gas appreciably. Quantities such as the time dependence of the formation of H2 molecules, the final H2 fraction, and central densities from the simulations are compared to the theoretical predictions of Abel (1995) and Tegmark et al. (1997) and found to agree remarkably well. Comparing the 3-D results to an isobaric collapse model we further discuss the possible implications of the extensive merging of small structure that is inherent in hierarchical models. Typically only 5-8% percent of the total baryonic mass in the collapsing structures is found to cool significanlty. Assuming the Padoan (1995) model for star formation our results would predict the first stellar systems to be as small as ~30\Ms. Some implications for primordial globular cluster formation scenarios are also discussed.

astro-ph↗