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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…
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…