Kardar, Parisi and Zhang introduced a universality class (the so-called KPZ universality class) in 1986 which is believed to explain the universal behaviour in a large class of two dimensional random growth models including first and last passage
Abstract: By Ramsey's theorem, any system of n segments in the plane has roughly log $n$ members that are either pairwise disjoint or pairwise intersecting.
Abstract: A basic problem in combinatorics is to determine the independence number of a hypergraph. We will consider this question in various contexts.
Abstract: Let B be standard Brownian motion. Fix an interval (a,b). Condition on B(t) to be in (a,b). Look at B(u) for u<.=t and B(u) u>.=t. We show that this converges weakly to a proper probability measure on C(R).
We present a new approach to showing that random graphs are nearly optimal expanders. This approach is based on deep results from combinatorial group theory. It applies both to regular and irregular random graphs.
