Related papers: Central Limit Theorems for the Brownian motion on …
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…
We consider the number of crossings in a random embedding of a graph, $G$, with vertices in convex position. We give explicit formulas for the mean and variance of the number of crossings as a function of various subgraph counts of $G$.…
A simple random walk and a Brownian motion are considered on a spider that is a collection of half lines (we call them legs) joined in the origin. We give a strong approximation of these two objects and their local times. For fixed number…
We consider the noncolliding Brownian motion (BM) with $N$ particles starting from the eigenvalue distribution of Gaussian unitary ensemble (GUE) of $N \times N$ Hermitian random matrices with variance $\sigma^2$. We prove that this process…
We consider n non-intersecting Brownian motion paths with p prescribed starting positions at time t=0 and q prescribed ending positions at time t=1. The positions of the paths at any intermediate time are a determinantal point process,…
We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimensional operator process with monotone and antimonotone…
We study random uniform permutations in an important class of pattern-avoiding permutations: the separable permutations. We describe the asymptotics of the number of occurrences of any fixed given pattern in such a random permutation in…
We give a simple proof of a central limit theorem for linear statistics of the Circular beta-ensembles which is valid at almost arbitrary mesoscopic scale and for functions of class C^3. As a consequence, using a coupling introduced by…
In this paper, we present the asymptotic theory for integrated functions of increments of Brownian local times in space. Specifically, we determine their first-order limit, along with the asymptotic distribution of the fluctuations. Our key…
We consider Dyson Brownian motion for classical values of $\beta$ with deterministic initial data $V$. We prove that the local eigenvalue statistics coincide with the GOE/GUE in the fixed energy sense after time $t \gtrsim 1/N$ if the…
In this paper we study mesoscopic fluctuations for Dyson's Brownian motion with $\beta=2$. Dyson showed that the Gaussian Unitary Ensemble (GUE) is the invariant measure for this stochastic evolution and conjectured that, when starting from…
We construct the full edge scaling limit of the singular values of Brownian motion on the general linear group $\mathsf{GL}_N(\mathbb{C})$ starting from general conditions. We show that the limiting paths solve an infinite system of SDE…
Representation theory and the theory of symmetric functions have played a central role in Random Matrix Theory in the computation of quantities such as joint moments of traces and joint moments of characteristic polynomials of matrices…
We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing…
In this paper we present a computation of the mean first-passage times both for a random walk in a discrete bounded lattice, between a starting site and a target site, and for a Brownian motion in a bounded domain, where the target is a…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then…
This paper presents a new approach to the analysis of mixed processes \[X_t=B_t+G_t,\qquad t\in[0,T],\] where $B_t$ is a Brownian motion and $G_t$ is an independent centered Gaussian process. We obtain a new canonical innovation…
This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…
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…