Random Walk: A Modern Introduction

By Gregory F. Lawler, V. Limic. 2010

937 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability, Signal Processing

View Paper: https://www.semanticscholar.org/paper/99c53efba62e6febddbd89bb87c3acb0eaa02983

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Citations in the corpus

Random Walks and Heat Kernels on Graphs (2017, background): “In the case where the random walk is on Z, there is a rich theory (see [8,14]) whose main message is that under diffusive scaling (multiplying by 1 √ n at time n) the random walk converges to a Gaussian distribution.”
A Survey of Knowledge Graph Reasoning on Graph Types: Static, Dynamic, and Multi-Modal (2022, background): “Random walk [146] inferences have been widely investigated.”
HAWKES PROCESSES ON LARGE NETWORKS (2016, neutral): “…[29, Theorem 2.1.1 and (2.5)] that there is a constant C such that for all n ≥ 1, all i ∈ Z d , where, for t > 0 and x ∈ R d , (21) To apply [29, Theorem 2.1.1], we needed to compute the covariance matrix Γ corresponding to our random walk, we found Γ = 2(2 d + 1) − 1 I d , I d being the d…”
Gaussian multiplicative chaos and applications: A review (2013, background): “; E[X (x)X (y)] = Eb x c[ ˝X@D i=1 1 S i=b y c] where (S i) i> 1 is the simple random walk in Z2 starting from bx cand ˝ @D stands for the rst exit time of the random walk out of D . By [100], we have the following expression: E[X (x)X (y)] = X z2@D Pbx c(S ˝ @D = z)a(zb y c) a(b x cb y c) w”
Price Dynamics in a Markovian Limit Order Market (2011, background): “(8) with the boundary conditions: ˚(0;p) = 0 for all p1 and ˚(n;0) = 1 for all n1. This problem is known as the discrete Dirichlet problem; solutions of (8) are called discrete harmonic functions. (Lawler and Limic 2010, Ch. 8) show that for all t0, the functions ft(x;y)=exr(t) sin(yt); and f~ t(x;y”