Related papers: Bessel process, Schramm-Loewner evolution, and Dys…
We show a finite-time large deviation principle (LDP) for "Dyson type" diffusion processes, including Dyson Brownian motion on the circle, for a fixed number of particles as the coupling parameter $\beta=8/\kappa$ tends to $\infty$. We also…
Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features…
We use the interpretation of the Schramm-Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of $n$-radial SLE going to a particular point. In order to justify the definition we prove that…
The two-dimensional Loewner exploration process is generalized to the case where the random force is self-similar with positively correlated increments. We model this random force by a fractional Brownian motion with Hurst exponent $H\geq…
We introduce a new diffusion process which arises as the $n\to\infty$ limit of a Bessel process of dimension $d \ge 2$ conditioned upon remaining bounded below one until time $n$. In addition to being interesting in its own right, we argue…
Modeling relaxation phenomena in complex media is central to understanding multiscale dynamics in materials science, bioengineering and condensed matter physics. Existing fractional-order models, while flexible, sometimes lack physical…
We consider a Feller diffusion (Zs, s $\ge$ 0) (with diffusion coefficient $\sqrt$ 2$\beta$ and drift $\theta$ $\in$ R) that we condition on {Zt = at}, where at is a deterministic function, and we study the limit in distribution of the…
This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching…
We establish universality for the largest singular values of products of random matrices with right unitarily invariant distributions, in a regime where the number of matrix factors and size of the matrices tend to infinity simultaneously.…
Prompted by an example arising in critical percolation, we study some reflected Brownian motions in symmetric planar domains and show that they are intertwined with one-dimensional diffusions. In the case of a wedge, the reflected Brownian…
We consider inhomogeneous branching diffusions on an infinite domain of $\mathbb{R}^d$. The first aim of this article is to derive a general criterium under which the size process (number of particles) and the genealogy of the particle…
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in…
We disclose the origin of anisotropic percolation perimeters in terms of the Stochastic Loewner Evolution (SLE) process. Precisely, our results from extensive numerical simulations indicate that the perimeters of multi-layered and directed…
We study Bessel and Dunkl processes $(X_{t,k})_{t\ge0}$ on $\mathbb R^N$ with possibly multivariate coupling constants $k\ge0$. These processes describe interacting particle systems of Calogero-Moser-Sutherland type with $N$ particles. For…
We develop a class of nonlocal delay Reaction-Diffusion (RD) models in a circular domain. Previous modeling efforts include RD population models with respect to one-dimensional unbounded domain, unbounded strip and rectangular spatial…
In this paper we pursue and complete the study of the simulation of the hitting time of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous…
We study the Besov regularity of wavelet series on $\mathbb{R}^d$ with randomly chosen coefficients. More precisely, each coefficient is a product of a random factor and a parameterized deterministic factor (decaying with the scale $j$ and…
Starting from the standard three-dimensional (3D) Gross-Pitaevskii equation (GPE) and using a variational approximation, we derive an effective one-dimensional nonpolynomial Schr\"odinger equation (1D-NPSE) governing the axial dynamics of…
In this paper, we define the squared G-Bessel process as the square of the modulus of a class of G-Brownian motions and establish that it is the unique solution to a stochastic differential equation. We then derive several path properties…
This paper studies two related stochastic processes driven by Brownian motion: the Cox-Ingersoll-Ross (CIR) process and the Bessel process. We investigate their shared and distinct properties, focusing on time-asymptotic growth rates,…