Consider a collection of N Brownian bridges B_i:-N,N→R, B i (− N)= B i (N)= 0, 1≤ i≤ N,
conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a …

We study systems of stochastic differential equations describing positions x_1,...,x_p of p
ordered particles, with inter-particles repulsions of the form H_ij(x_i,x_j)/(x_i-x_j). We show …

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 …

We prove a multidimensional version of the Yamada-Watanabe theorem, ie, a theorem
giving conditions on coefficients of a stochastic differential equation for existence and …

We prove tail triviality of determinantal point processes μ μ on continuous spaces. Tail
triviality has been proved for such processes only on discrete spaces, and hence we have …

The singular values squared of the random matrix product Y= G_ r G_ r-1 ... G_ 1 (G_ 0+ A)
Y= G r G r-1… G 1 (G 0+ A), where each G_ j G j is a rectangular standard complex …

We consider the double scaling limit for a model of n non-intersecting squared Bessel
processes in the confluent case: all paths start at time t= 0 at the same positive value x= a …

We study the Fredholm determinant of an integral operator associated to the hard edge
Pearcey kernel. This determinant appears in a variety of random matrix and nonintersecting …

We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so
that in particular the motion can be space-inhomogeneous, interacting via one-sided …

We study the strong existence and uniqueness of solutions within a Weyl chamber for a
class of time-dependent particle systems driven by multiplicative noise. This class includes …