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Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper we show that ensembles of entwined paths on a discrete space-time lattice are simply…
Adaptive importance sampling is a class of techniques for finding good proposal distributions for importance sampling. Often the proposal distributions are standard probability distributions whose parameters are adapted based on the…
Let D(n,p) be the random directed graph on n vertices where each of the n(n-1) possible arcs is present independently with probability p. A celebrated result of Frieze shows that if $p\ge(\log n+\omega(1))/n$ then D(n,p) typically has a…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We show that residence time measure can be used to identify the geometrical and transmission properties of a defect along a path. The model we study is based on a one--dimensional simple random walk. The sites of the lattice are regular,…
In probability theory, reinforced walks are random walks on a lattice (or more generally a graph) that preferentially revisit neighboring `locations' (sites or bonds) that have been visited before. In this paper, we consider walks with…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence.…
Take a centered random walk S_n and consider the sequence of its partial sums A_n = S_1 + ... + S_n. Suppose S_1 is in the domain of normal attraction of an \alpha-stable law with 1 < \alpha <= 2. Assuming that S_1 is either…
We study random spatial permutations on Z^3 where each jump x -> \pi(x) is penalized by a factor exp(-T ||x-\pi(x)||^2). The system is known to exhibit a phase transition for low enough T where macroscopic cycles appear. We observe that the…
The signature transform is a 'universal nonlinearity' on the space of continuous vector-valued paths, and has received attention for use in machine learning on time series. However, real-world temporal data is typically observed at discrete…
Interacting particle systems with many degrees of freedom may undergo phase transitions to sustain atypical fluctuations of dynamical observables such as the current or the activity. This leads in some cases to symmetry-broken space-time…
The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability…
The transition probability for a one-dimensional discrete symmetric random walk under a reflecting barrier was once given by the method of images. [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).] However, several inconsistencies have been…
The spatial coverage produced by a single discrete-time random walk, with asymmetric jump probability $p\neq 1/2$ and non-uniform steps, moving on an infinite one-dimensional lattice is investigated. Analytical calculations are complemented…
We study the escape probability problem in random walks over graphs. Given vertices, $s,t,$ and $p$, the problem asks for the probability that a random walk starting at $s$ will hit $t$ before hitting $p$. Such probabilities can be…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
This paper focuses on generating test cases from timed symbolic transition systems. At the heart of the generation process are symbolic execution techniques on data and time. Test cases look like finite symbolic trees with verdicts on their…
We present results from extensive simulations of driven vortex lattices interacting with periodic arrays of pinning sites. Changing an applied driving force produces a rich variety of novel dynamical plastic flow phases which are very…
The first passage statistics of a continuous time random walker with Poisson distributed jumps on one and two dimensional infinite lattices is investigated. An exact expression for the probability of first return to the origin in one…