# Random walk with different directions

## Simao Herdade, Rutgers University

## November 3, 2015

We study a random walk where all steps have same length but different
directions. Using recent results from inverse Littlewood-Offord theory
(of
Nguyen, Tao, and Vu) we obtain a sharp bound for the maximum returning
probability of such random walks, for any dimension other than $d=3$.
In the euclidean space, we pose a new conjecture in Discrete
Geometry,
from which an analogous bound would follow.

Joint work with Van Vu.