Random walks on FKG-horizontally oriented lattices

随机过程的若干FKG不等式

Some FKG inequalities for stochastic processes

本文利用Markov chains和random walks的逼近方法，证明了连续时间下Lévy过程、Bessel过程等随机过程的FKG型相关不等式，并给出了$\bbZ$上random walk分布满足FKG格条件的充要条件。

Collision times of random walks and applications to the Brownian web

Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes, Isopi, Newman and Ravishankar (2004). One of their convergence condition, called (B2), states that the probability of the event that there exists three distinct paths for a time interval of length $t(>0)$, all starting within a segment of length $\varepsilon$, is of small order of $\varepsilon$. This condition is often verified by applying an FKG type correlation in…

通过Russo-Seymour-Welsh方法得到的动态环境中对称随机游走的涨落下界

Fluctuation bounds for symmetric random walks on dynamic environments via Russo-Seymour-Welsh

本文在1+1维动态随机环境的弱影响微扰区域中，利用受渗流理论启发的RSW不等式，为满足平移反射不变性、FKG不等式及温和混合条件的对称随机游走证明了涨落下界，并以高斯场和Confetti渗流模型为例说明结果的普适性。

Random walks on randomly oriented lattices

Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the orientation the asymptotic behaviour of the random walk is shown to be recurrent or transient. In particular, for randomly horizontally oriented lattices the random walk is almost surely transient.

Planar random walk in a stratified quasi-periodic environment

We study the recurrence of inhomogeneous Markov chains in the plane, when the environment is horizontally stratified and the heterogeneity of quasi-periodic type.

Power law Polya's urn and fractional Brownian motion

We introduce a natural family of random walks on the set of integers that scale to fractional Brownian motion. The increments X_n have the property that given {X_k: k < n}, the conditional law of X_n is that of X_{n-k_n}, where k_n is sampled independently from a fixed law μon the positive integers. When μhas a roughly power law decay (precisely, when it lies in the domain of attraction of an αstable subordinator, for 0 < α< 1/2) the walk scales to fractional Brownian motion with Hurst parameter α+ 1/2. The walks are easy to simulate and their increments satisfy an FKG inequality. In a sense w…