Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.13518

The inertial Itô drift and its applications to particle collision

Sandra Cerrai·Franco Flandoli·Mengzi Xie
View original source ↗Read source document ↗Export metadata ↓

Abstract

The small mass $μ$ limit of an inertial system driven by an Ornstein Uhlenbeck fluid force, with correlation time $ε$ going to zero, leads to a first order system with an additional drift, which we call inertial-Itô-drift, depending on the limit $α$ of the ratio $μ/ε$; the drift being zero when $α=0$, corresponding to the Stratonovich integral in the limit equation, as in the Wong-Zakai theory, when applied directly to the first-order system with Ornstein-Uhlenbeck driver. We discuss the application of this result to particles driven by Stokes force;\ we identify inertial centrifugal effects and the so-called turbophoretic effect, as examples of the inertial-Itô-drift. We also analyze concentration effects and their link with the theory of particle collision in turbulent fluids.

Explore related subjects

math.PR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sandra Cerrai, Franco Flandoli, Mengzi Xie. 2026-05-13. The inertial Itô drift and its applications to particle collision. https://arxiv.org/abs/2605.13518

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Generalized Edgeworth expansions for integer-valued additive functionals of uniformly elliptic Markov chains

We obtain asymptotic expansions for probabilities $\bbP(S_N=k)$ of partial sums of uniformly bounded integer-valued functionals $\DS S_N=\sum_{n=1}^N f_n(X_n)$ of uniformly elliptic inhomogeneous Markov chains. The expansions involve products of polynomials and trigonometric polynomials, and they hold without additional assumptions. As an application of the explicit formulas of the trigonometric polynomials, we relate existence of the standard Edgeworth expansions of order $r$ to the rate of equidistributions of $S_N$ modulo $m$ for small positive integers $m.$

math.PR↗
arXiv2026

Permutations from Random Walk

Xavier and Yushi run a "random race" as follows. An atomless probability distribution $μ$ on the real line is chosen. The runners begin at zero. At time $i$ Xavier draws $\mathbf{X}_i$ from $μ$ and advances that distance, while Yushi advances by an independent drawing $\mathbf{Y}_i$. After $n$ such moves, what is the probability that Yushi led all the way? That the answer (namely, $4^{-n}\binom{2n}{n}$) is independent of $μ$ follows from a classical theorem of Darling, stating that for symmetric atomless increments, the distribution of each individual rank in the permutation obtained by ranking the partial sums is independent of the step law. We give a self-contained proof and extend the result to the permutations generated by partial sums of uniformly random signed permutations of any fixed, finite, generic set of reals. For atomless increments with mean zero and finite variance, without assuming symmetry, we show that random-walk permutations approach a random object that we call the "Wiener permuton," whose expected pattern densities equal the probabilities of the corresponding permutations generated by finite random walks with centered Laplace increments. Finally, we exhibit an infinite family of constructions whose limiting permutons interpolate between the Wiener permuton and the recursive separable permuton; each has the same intensity permuton, providing a single two-dimensional extension of the classical arcsine law for all of them.

math.PR↗
arXiv2026

On the uniqueness of quasi-stationary distributions for population models with spatial structure

Subcritical population processes are attracted to extinction and do not have non-trivial stationary distributions, which prompts the study of quasi-stationary distributions (QSDs) instead. In contrast to what generally happens for stationary distributions, QSDs may not be unique, even under irreducibility conditions. The general conditions for uniqueness of QSDs are not always easy to check. For the branching process, besides the quasi-limiting distribution there are many other QSDs. In this paper, we investigate whether adding little extra information to the continuous-time branching process is enough to obtain uniqueness. We consider the branching process with genealogy and branching random walks, and show that they have a unique QSD.

math.PR↗