Related papers: Compressed self-avoiding walks, bridges and polygo…
The critical behaviour of directed self-avoiding walks is studied on parabolic-like systems with a free boundary at x=\pm Ct^\alpha. Using a scaling argument, 1/C is shown to be a marginal variable when \alpha=\nu_\perp/\nu_\parallel=1/2,…
We recently published [J. Phys A: Math. Theor. {\bf 45} 115202 (2012)] a new and more efficient implementation of a transfer-matrix algorithm for exact enumerations of self-avoiding polygons. Here we extend this work to the enumeration of…
We consider a multi-walker generalization of the true self-avoiding walk: the bricklayer model. We perform stochastic simulations, and solve the partial differential equations that describe the collective motion of $N$ bricklayers/walkers…
We analyze the Brownian Motion limit of a prototypical unit step reinforced random-walk on the half line. A reinforced random walk is one which changes the weight of any edge (or vertex) visited to increase the frequency of return visits.…
Let $X_i = {X_i(t), t \in T}$ be i.i.d. copies of a centered Gaussian process $X = {X(t), t \in T}$ with values in $\mathbb{R}^d$ defined on a separable metric space $T.$ It is supposed that $X$ is bounded. We consider the asymptotic…
Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \emph{$k$-sided prudent walks} (with $k=1,2,3,4$) are, in essence, only allowed to grow along $k$ directions. Prudent polygons are…
We give a survey and unified treatment of functional integral representations for both simple random walk and some self-avoiding walk models, including models with strict self-avoidance, with weak self-avoidance, and a model of walks and…
In two dimensions polymer collapse has been shown to be complex with multiple low temperature states and multi-critical points. Recently, strong numerical evidence has been provided for a long-standing prediction of universal scaling of…
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…
As a model of trapping by biased motion in random structure, we study the time taken for a biased random walk to return to the root of a subcritical Galton-Watson tree. We do so for trees in which these biases are randomly chosen,…
Although visual search appears largely random, several oculomotor biases exist such that the likelihoods of saccade directions and lengths depend on the previous scan path. Compared to the most recent fixations, the impact of the longer…
The motion of l=0 antibound poles of the S-matrix with varying potential strength is calculated in a cutoff Woods-Saxon (WS) potential and in the Salamon-Vertse (SV) potential, which goes to zero smoothly at a finite distance. The pole…
We study the behaviour of a class of edge-reinforced random walks {on $\mathbb{Z}_+$}, with heterogeneous initial weights, where each edge weight can be updated only when the edge is traversed from left to right. We provide a description…
For $d \geq 2$ and $n \in \mathbb{N}$, let $\mathsf{W}_n$ denote the uniform law on self-avoiding walks of length $n$ beginning at the origin in the nearest-neighbour integer lattice $\mathbb{Z}^d$, and write $\Gamma$ for a…
Reasoning about distance is indispensable for establishing or avoiding contact in manipulation tasks. To this end, we present an online approach for learning implicit representations of signed distance using piecewise polynomial basis…
We consider a one-dimensional random walk among biased i.i.d. conductances, in the case where the random walk is transient but sub-ballistic: this occurs when the conductances have a heavy-tail at $+\infty$ or at $0$. We prove that the…
In this article we study a one dimensional model for a polymer in a poor solvent: the random walk on $\mathbb{Z}$ penalized by its range. More precisely, we consider a Gibbs transformation of the law of the simple symmmetric random walk by…
We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate…
Self-avoiding walks self-interacting via nearest neighbours (ISAW) and self-avoiding trails interacting via multiply-visited sites (ISAT) are two models of the polymer collapse transition of a polymer in dilute solution. On the square…
We consider a recent model of random walk that recursively grows the network on which it evolves, namely the Tree Builder Random Walk (TBRW). We introduce a bias $\rho \in (0,\infty)$ towards the root, and exhibit a phase transition for…