ﻻ يوجد ملخص باللغة العربية
We show that the squared maximal height of the top path among $N$ non-intersecting Brownian bridges starting and ending at the origin is distributed as the top eigenvalue of a random matrix drawn from the Laguerre Orthogonal Ensemble. This result can be thought of as a discrete version of K. Johanssons result that the supremum of the Airy$_2$ process minus a parabola has the Tracy-Widom GOE distribution, and as such it provides an explanation for how this distribution arises in models belonging to the KPZ universality class with flat initial data. The result can be recast in terms of the probability that the top curve of the stationary Dyson Brownian motion hits an hyperbolic cosine barrier.
In this paper we study a certain recurrence relation, that can be used to generate ladder operators for the Laguerre Unitary ensemble, from the point of view of Sakais geometric theory of Painleve equations. On one hand, this gives us one more detail
In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from $a_1leq a_2leq cdots leq a_n$ at time $t=0$ and ending at $b_1leq b_2leq cdotsleq b_n$ at time $t=1$, where $mu_{A_n}=(1/n)sum_{i}delta_{a_i},
The Brownian web (BW), which developed from the work of Arratia and then T{o}th and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space-time that arises as the scaling limit of the discrete web (
We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general beta siblings converge to Sine_beta, a translation invariant point process. This process has a geometric description in term of
We study geodesics in the Brownian map $(mathcal{S},d, u)$, the random metric measure space which arises as the Gromov-Hausdorff scaling limit of uniformly random planar maps. Our results apply to all geodesics including those between exceptional poi