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安徽师范大学概率论与数理统计课件Chapter4 Limit Theorems
We use the existence of localized eigenfunctions of the Laplacian on the Sierpinski gasket (SG) to formulate and prove analogues of the strong Szego limit theorem in this fractal setting.Furthermore, ...
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 study the asymptotic behaviour of occupation times of a transient random walk in a quenched random environment on a strip in a sub-di usive regime. The asymptotic behaviour of hitting times, whic...
We consider random walks (RW) in a one-dimensional i.i.d. random environment with jumps to the nearest neighbours. For almost all environments, we prove a quenched Local Limit Theorem (LLT) for the...
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...
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...
One of the major discoveries of the 20th century mathematics is the possibility of random behavior of deterministic systems. There is a hierarchy of chaotic properties for a dynamical systems but on...
We consider a large class of partially hyperbolic systems containing, among others, ane maps, frame ows on negatively curved manifolds and mostly contracting di eomorphisms. If the rate of mixing ...
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’...
We study the scaling limits of three different aggregation models on Zd: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which parti...
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 ...
We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = f1;2; : : : ; ng. The arguments use a novel stochastic representation and are also ...

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