1 citations · 1 across the 4 of their papers we have counts for
7 papers
Non-colliding billiards in the plane
Itai Benjamini, Alexander Shamov, Barak Weiss
We present an open problem about non-colliding freely moving hard disks in the Euclidean plane, together with related positive and negative partial results. The open problem is sta…
Kernels of conditional determinantal measures and the proof of the Lyons-Peres Conjecture
Alexander I. Bufetov, Yanqi Qiu, Alexander Shamov
The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels s…
Where does a random process hit a fractal barrier?
Itai Benjamini, Alexander Shamov
Given a Brownian path on , starting at , a.s. there is a singular time set , such that the first hitting time of by an independent Brownian motion, s…
Weak and Strong disorder for the stochastic heat equation and the continuous directed polymer in
Chiranjib Mukherjee, Alexander Shamov, Ofer Zeitouni
We consider the smoothed multiplicative noise stochastic heat equation $$d u_{\eps,t}= \frac 12 Δu_{\eps,t} d t+ β\eps^{\frac{d-2}{2}}\, \, u_{\eps, t} \, d B_{\eps,t} , \;\;u_{\ep…
Bi-Lipschitz bijections of
Itai Benjamini, Alexander Shamov
It is shown that every bi-Lipschitz bijection from to itself is at a bounded distance from either the identity or the reflection. We then comment on the g…
On Gaussian multiplicative chaos
Alexander Shamov
We propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized shifts of a Gaussian measure. Using th…
On short-time asymptotics of one-dimensional Harris flows
Alexander Shamov
We study the short-time asymptotical behavior of stochastic flows on \mathbb{R} in the \sup-norm. The results are stated in terms of a Gaussian process associated with the covariat…