Abundance of Maximal Paths
Vladas Sidoravicius
ABSTRACT:
We show that in the Bernoulli oriented last-passage percolation problem on the positive
quadrant of the d-dimensional hypercubic lattice, with probability exponentially close
to 1, the number of maximizing paths from the origin to the hyperplane H_n grows
exponentially in n. This fact is widely believed and used as an important technical tool
in the theoretical physics literature in studies of a variety of disordered systems such
as First/Last Passage Percolation type growth models, directed polymers in random
environment. However, in spite of its wide acceptance, and apparent simplicity, all previous
attempts to prove this fact have failed.
(Joint work with H. Kesten, F. Nazarov and Y. Peres.)
BIO:
Vladas Sidoravicius is a Professor in IMPA (Rio de Janeiro) and in CWI (Amsterdam). He
is concluding a six week visit to MSR. His main interests are in Probability Theory
and Statistical Physics, especially Random walks in Random Environment, Percolative systems,
Phase transitions and Renormalization Group Methods. At any moment in time, you can either
determine where he is, or where he is going next, but not both.