As an extension of the theory of Dyson's Brownian motion models for the standard Gaussian
random-matrix ensembles, we report a systematic study of Hermitian matrix-valued …

We consider the stochastic evolution of three variants of the RSK algorithm, giving both
analytic descriptions and probabilistic interpretations. Symmetric functions play a key role …

A system of one-dimensional Brownian motions (BMs) conditioned never to collide with
each other is realized as (i) Dyson's BM model, which is a process of eigenvalues of …

This book is based on my graduate-course lectures given at the Graduate School of
Mathematics of the University of Tokyo in October 2008 (at the invitation of T. Funaki and M …

One-dimensional Brownian motion starting from the origin at time t= 0, conditioned to return
to the origin at time t= 1 and to stay positive during time interval 0< t< 1, is called the Bessel …

A noncolliding diffusion process is a conditional process of $ N $ independent one-
dimensional diffusion processes such that the particles never collide with each other. This …

Non-colliding Brownian particles in op. e dimension is studied. N Brownian particles start
from the origin at time 0 and then they do not collide with each other until finite time T. We …

We derive asymptotics for the moments as well as the weak limit of the height distribution of
watermelons with p branches with wall. This generalizes a famous result of de Bruijn et al …

We perform an exact and asymptotic analysis of the model of n vicious walkers interacting
with a wall via contact potentials, a model introduced by Brak, Essam and Owczarek. More …

Yor's generalized meander is a temporally inhomogeneous modification of the 2 (ν+ 1)-
dimensional Bessel process with ν>− 1, in which the inhomogeneity is indexed by κ ∈ 0, 2 …