Related papers: Simulating self-avoiding walks in bounded domains
The scaling behavior of linear polymers in disordered media modelled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p_c is studied. All possible SAW…
We study self-avoiding walks on restricted square lattices, more precisely on the lattice strips $\mathbb{Z} \times \{-1,0,1\}$ and $\mathbb{Z}\times \{-1,0,1,2\}$. We obtain the value of the connective constant for the $\mathbb{Z} \times…
The pseudo-marginal algorithm is a variant of the Metropolis--Hastings algorithm which samples asymptotically from a probability distribution when it is only possible to estimate unbiasedly an unnormalized version of its density.…
We consider a new model of a branching random walk on a multidimensional lattice with continuous time and one source of particle reproduction and death, as well as an infinite number of sources in which, in addition to the walk, only…
We study the range $R_n$ of a random walk on the $d$-dimensional lattice $\mathbb{Z}^d$ indexed by a random tree with $n$ vertices. Under the assumption that the random walk is centered and has finite fourth moments, we prove in dimension…
Autonomous robots operating in indoor and GPS denied environments can use LiDAR for SLAM instead. However, LiDARs do not perform well in geometrically-degraded environments, due to the challenge of loop closure detection and computational…
Existing methods for avoiding dynamic engagement zones (EZs) and minimizing risk leverage the calculus of variations to obtain optimal paths. While such methods are deterministic, they scale poorly as the number of engagement zones…
Random walks can be used to search complex networks for a desired resource. To reduce search lengths, we propose a mechanism based on building random walks connecting together partial walks (PW) previously computed at each network node.…
We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted…
We have developed a parallel algorithm that allows us to enumerate the number of self-avoiding polygons on the square lattice to perimeter length 110. We have also extended the series for the first 10 area-weighted moments and the radius of…
We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…
Bayesian modelling enables us to accommodate complex forms of data and make a comprehensive inference, but the effect of partial misspecification of the model is a concern. One approach in this setting is to modularize the model, and…
Deep reinforcement learning algorithms typically act on the same set of actions. However, this is not sufficient for a wide range of real-world applications where different subsets are available at each step. In this thesis, we consider the…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
We study branching random walks in random environment on the $d$-dimensional square lattice, $d \geq 1$. In this model, the environment has finite range dependence, and the population size cannot decrease. We prove limit theorems (laws of…
This thesis examines linearly edge-reinforced random walks on infinite trees. In particular, recurrence and transience of such random walks on general (fixed) trees as well as on Galton-Watson trees (i.e. random trees) is characterized, and…