Sasha Sodin

NON-BACKTRACKING RANDOM WALKS MIX FASTER

We compute the mixing rate of a non-backtracking random walk on a regular expander. Using some properties of Chebyshev polynomials of the second kind, we show that this rate may be up to twice as fast as the mixing rate of the simple random walk. The closer the expander is to a Ramanujan graph, the higher the ratio between the above two mixing rates is. As an application, we show that if G is a high-girth regular expander on n vertices, then a typical non-backtracking random walk of length n on G does not visit a vertex more than times, and this result is tight. In this sense, the multi-set of visited vertices is analogous to the result of throwing n balls to n bins uniformly, in contrast to the simple random walk on G, which almost surely visits some vertex Ω(log n) times.

An isoperimetric inequality on the ℓp balls

The normalised volume measure on the

The Tracy–Widom Law for Some Sparse Random Matrices

\ell_p^n

Localisation for non-monotone Schrödinger operators

unit ball (

Random matrices, nonbacktracking walks, and orthogonal polynomials

1\leq p\leq 2

Tail-Sensitive Gaussian Asymptotics for Marginals of Concentrated Measures in High Dimension

) satisfies the following isoperimetric inequality: the boundary measure of a set of measure

Polynomial bounds for Large Bernoulli sections of ℓ1N

a

An Analytical Approach to the Calculation of EVM in Clipped Multi-Carrier Signals

is at least

An Estimate for the Average Spectral Measure of Random Band Matrices

cn^{1/p}\tilde{a}\log^{1-1/p}(1/\tilde{a})

Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

, where