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I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
This talk mainly concerns the projective, Moishezon and Kahler loci of a family. We first introduce four conjectures on this topic and then the works of the deformation limit of projective manifolds a...
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 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 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...
We study a particle moving in R 2 under a constant (external) force and bouncing off a periodic array of convex domains (scatterers); the latter must satisfy a standard ‘finite horizon’...
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. The limit theorems are universal depending solely on the limiting behavior ...
Let (M, g) be a compact Riemannian manifold on which a tracefree and divergence-free  2 W1,p and a positive function  2 W1,p, p > n,are fixed. In this paper, we study the vacuum Einstein constraint ...

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