arXiv subjects

Kyprianos-Iason Prodromidis

Publications and source records attributed to Kyprianos-Iason Prodromidis.

5 recordsLinked to original sources

arXiv2026

Cutoff profile for the balanced generalized Bernoulli--Laplace model

We study the balanced generalized Bernoulli--Laplace model introduced by Goenka, Hermon, and Schmid (2025) and establish a Gaussian cutoff profile under spectral conditions satisfied by all reversible chains and the cyclic shift chain. Our method adapts the approach of Olesker-Taylor and Schmid (2026) for the two-urn model, combining concentration around a deterministic trajectory before the cutoff window with an Ornstein--Uhlenbeck approximation near equilibrium. We also give an instance of this model that exhibits cutoff but has no limit profile. Further, we determine the mixing time up to an additive constant for every irreducible instance of the model, identifying a $\log \log n$ correction governed by the largest Jordan block size corresponding to the slowest decaying modes.

math.PR↗

arXiv2026

Distribution of the magnetization of the critical Ising model on sparse random graphs

In this paper, we consider the Ising model on random $d$-regular graphs (with $d\ge3$) and Erdös-Rényi graphs $G(n,d/n)$ (with $d>1$) at the critical temperature. We prove that the \textit{magnetization}, i.e.\ the sum of the spins of a configuration, is typically of order $n^{3/4}$ and when multiplied by $n^{-3/4}$ converges in distribution to a non-trivial random variable, whose density we describe. In the regular graph case, the Small Subgraph Conditioning Method applies, and the limiting density is of the form $\frac1{Z}\exp(-C_d z^4)$. Surprisingly, in the Erdös-Rényi case, while the ratio of the second moment and first moment squared is bounded, the short cycle count is not enough to explain the fluctuations of the partition function restricted to a particular magnetization. We identify the additional source of randomness as path counts of slowly diverging length. This quantity is motivated by the heuristic that correlations between distant vertices are proportional to their local branching rate. Augmenting the Small Subgraph Conditioning Method with these path counts allows us to prove convergence of the magnetization to a non-deterministic limiting distribution. To our knowledge, the need to condition on graph observables beyond the cycle counts is a new phenomenon for spin systems. As further corollaries, we derive a polynomial lower bound on the mixing time of the stochastic Ising model on sparse random graphs at the critical temperature complementing recent upper bounds. Moreover, we establish the fluctuations of the free energy in the Erdös-Rényi case, answering a recent question of Coja-Oghlan et. al.

math.PR↗

arXiv2025

Limit Profile for the high-temperature Curie-Weiss model

In this paper, we consider the Ising model on the complete graph, also known as the Curie-Weiss model, and establish the limit profile of the Glauber dynamics in the high-temperature regime. Our strategy is a two-dimensional analog of the method developed by Olesker-Taylor and Schmid for the Bernoulli-Laplace urn: The two-coordinate chain associated to the model evolves near-deterministically until just before the cutoff window, while afterwards it approximates a two-dimensional diffusion.

math.PR↗

arXiv2025

Polynomial mixing of the critical Ising model on sparse Erdos-Renyi graphs

We consider the stochastic Ising model on sparse Erdos-Renyi graphs $G(n,d/n)$ with $d>1$ at the critical temperature $β_c=\tanh^{-1}(d^{-1})$ and prove that with high probability, the mixing time is at most polynomial in $n$. Our approach combines the recent stochastic localization framework of Chen and Eldan, which yields spectral gap bounds in the well-behaved bulk of the graph, together with classical results on the relaxation time of Glauber dynamics on trees to handle regions where we cannot apply the Chen-Eldan method directly because of atypically large local neighborhoods.

math.PR↗

arXiv2024

Polynomial Mixing of the critical Glauber Dynamics for the Ising Model

In this note, we prove that on any graph of maximal degree $d$ the mixing time of the Glauber Dynamics for the Ising Model at $β_c=\tanh^{-1}(\frac1{d-1})$, the uniqueness threshold on the infinite $d$-regular tree, is at most polynomial in $n$. The proof follows by a simple combination of new log-Sobolev bounds of Bauerschmidt and Dagallier, together with the tree of self avoiding walks construction of Weitz. While preparing this note we became aware that Chen, Chen, Yin and Zhang recently posted another proof of this result. We believe the simplicity of our argument is of independent interest.

math.PR↗