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This article studies large $N$ limits of a coupled system of $N$ interacting $\Phi^4$ equations posed over $\mathbb{T}^{d}$ for $d=2$, known as the $O(N)$ linear sigma model. Uniform in $N$ bounds on ...
Methods of merging several p-values into a single p-value are important in their own right and widely used in multiple hypothesis testing. This paper is the first to systematically study the admissibi...
In this paper, we justify the semiclassical limit of the Gross--Pitaevskii equation with Dirichlet boundary condition on the three-dimensional upper space under the assumption that the leading-order t...
本文研究了一类带有多项式谱参数边界条件的Sturm-Liouville问题的谱分析.通过构造,证明了这类问题具有有限谱且所有谱都是特征值.
Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statisti...
We prove that a recurrent random walk (RW) in i.i.d. random environment (RE) on a strip which does not obey the Sinai law exhibits the Central Limit asymptotic behaviour.
We describe scaling limits of recurrent excited random walks (ERWs) on Z in i.i.d. cookie environments with a bounded number of cookies per site. We allow both positive and negative excitations.
We consider excited random walk on a strip. We assume that the cookies are positive and that the total expected drift per site is less than 1/L where L is the width of the strip. We prove a quenched...
It is well known that random walks in one dimensional random environment can exhibit subdiffusive behavior due to presence of traps. In this paper we show that the passage times of diffe...
We prove a local limit the sums of independent random vectors satisfying appropriate tightness assumptions. In particular, the local limit theorem holds in dimension 1 if the summands are uniformly bo...
One of the surprising discoveries of dynamical systems theory is that many deterministic systems with non-zero Lyapunov exponents satisfy the same limit theorems as the sums of independent random v...
We study electrical current in two-dimensional periodic Lorentz gas in the presence of a weak homogeneous etric field.When the horizon is finite, i.e. the free flights between colli...
PRELUDE TO A KISS     KISS  limit       2015/9/29
We consider expanding maps of the circle with an almost neutral fixed point c. In this setting the ergodic averages of a smooth observable A satisfy the Central Limit Theorem. If A(c) = 0 we s...
We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t ...
Modify the scatterer conguration of a planar, nitehorizon Lorentz process in a bounded domain. Sinai asked in 1981 whether for the diffusively scaled variant of the modied process convergence to Bro...

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