Related papers: A generalised Airy distribution function for the a…
This paper gives a PDE for multi-time joint probability of the Airy process, which generalizes Adler and van Moerbeke's result on the 2-time case. As an intermediate step, the PDE for the multi-time joint probability of the Dyson Brownian…
The real trees form a class of metric spaces that extends the class of trees with edge lengths by allowing behavior such as infinite total edge length and vertices with infinite branching degree. Aldous's Brownian continuum random tree, the…
Gaussian distributions can be generalized from Euclidean space to a wide class of Riemannian manifolds. Gaussian distributions on manifolds are harder to make use of in applications since the normalisation factors, which we will refer to as…
We consider an $\epsilon K$ transversal perturbing vector field in a foliated Brownian motion defined in a foliated tubular neighbourhood of an embedded compact submanifold in $\R^3$. We study the effective behaviour of the system under…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an…
We consider vectors of random variables, obtained by restricting the length of the nodal set of Berry's random wave model to a finite collection of (possibly overlapping) smooth compact subsets of $\mathbb{R}^2$. Our main result shows that,…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
After different variables and functions changes, the generalized dispersal problem, recalled in (1) below and considered in part I, see [14], leads us to invert a sum of linear operators in a suitable Banach space, see (2) below. The…
We consider very general "random integers" and (attempt to) prove that many multiplicative and additive functions of such integers have limiting distributions. These integers include, for instance, the curvatures of Apollonian circle…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and…
Let v be a bounded function with bounded support in R^d, d>=3. Let x,y in R^d. Let Z(t) denote the path integral of v along the path of a Brownian bridge in R^d which runs for time t, starting at x and ending at y. As t->infty, it is…
For general $\beta \geq 1$, we consider Dyson Brownian motion at equilibrium and prove convergence of the extremal particles to an ensemble of continuous sample paths in the limit $N \to \infty$. For each fixed time, this ensemble is…
We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative…
We construct a coupling between the random walk composed of L\'evy area increments from a $d$-dimensional Brownian motion and a random walk composed of quadratic polynomials of Gaussian random variables. This coupling construction is used…
Time evolution of the position-velocity correlation functions (PVCF) plays a key role in a new formalism of Brownian motion. A system of differential equations, which governs PVCF, is derived for magnetic Skyrmions on a 2-dimensional…
Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center…
We study the convergence in rough path topology of a certain class of discrete processes, the hidden Markov walks, to a Brownian motion with an area anomaly. This area anomaly, which is a new object, keeps track of the time-correlation of…
We present an exact solution for one-dimensional overdamped dynamics near a hard wall, allowing us to connect steady-state distributions under confinement with the extreme value statistics of unconfined stochastic processes. This mapping…