This review addresses recent developments in non-equilibrium statistical physics. Focusing
on phase transitions from fluctuating phases into absorbing states, the universality class of …

We derive new results for the number of star and watermelon configurations of vicious
walkers in the presence of an impenetrable wall by showing that these follow from standard …

We rederive previously known results for the number of star and watermelon configurations
by showing that these follow immediately from standard results in the theory of Young …

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 …

A number, p, of vicious random walkers on a D-dimensional lattice is considered.''Vicious
walkers''describes the situation when two or more walkers arrive at the same lattice site and …

We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher
and derive a system of nonintersecting Brownian motions. The spatial distribution of N …

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 …

In his famous book\Combinatory Analysis" MacMahon introduced Partition Analysis as a
computational method for solving problems in connection with linear homogeneous …

It is known that the moments of the maximum value of a one-dimensional conditional
Brownian motion, the three-dimensional Bessel bridge with duration 1 started from the …

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 …