Related papers: Simulating self-avoiding walks in bounded domains
A celebrated problem in numerical analysis is to consider Brownian motion originating at the centre of a $10 \times 1$ rectangle, and to evaluate the ratio of probabilities of a Brownian path hitting the short ends of the rectangle before…
We consider self-avoiding walks (SAWs) on the backbone of percolation clusters in space dimensions d=2, 3, 4. Applying numerical simulations, we show that the whole multifractal spectrum of singularities emerges in exploring the…
We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at $(L, L)$, and are entirely contained in the square $[0, L] \times [0, L]$ on the square lattice ${\mathbb Z}^2$. The number of distinct walks…
A comprehensive numerical study of self-avoiding walks (SAW's) on randomly diluted lattices in two and three dimensions is carried out. The critical exponents $\nu$ and $\chi$ are calculated for various different occupation probabilities,…
We develop an approach for performing scaling analysis of $N$-step Random Walks (RWs). The mean square end-to-end distance, $\langle\vec{R}_{N}^{2}\rangle$, is written in terms of inner persistence lengths (IPLs), which we define by the…
The pivot algorithm for self-avoiding walks has been implemented in a manner which is dramatically faster than previous implementations, enabling extremely long walks to be efficiently simulated. We explicitly describe the data structures…
This paper analyzes a random walk model for the level lines appearing in the entropic repulsion phenomena of three-dimensional discrete random interfaces above a hard wall; we are particularly motivated by the low-temperature (2+1)D…
This article is concerned with self-avoiding walks (SAW) on $\mathbb{Z}^{d}$ that are subject to a self-attraction. The attraction, which rewards instances of adjacent parallel edges, introduces difficulties that are not present in ordinary…
We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…
We define a new family of self-avoiding walks (SAW) on the square lattice, called weakly directed walks. These walks have a simple characterization in terms of the irreducible bridges that compose them. We determine their generating…
We review the existence of the infinite length self-avoiding walk in the half plane and its relationship to bridges. We prove that this probability measure is also given by the limit as $\beta \rightarrow \beta_c-$ of the probability…
We present an analytical and numerical study of the paths of self avoiding walks (SAWs) on random networks. Since these walks do not retrace their paths, they effectively delete the nodes they visit, together with their links, thus pruning…
The $n$-vector spin model, which includes the self-avoiding walk (SAW) as a special case for the $n \rightarrow 0 $ limit, has an upper critical dimensionality at four spatial dimensions (4D). We simulate the SAW on 4D hypercubic lattices…
We construct the two-sided infinite self-avoiding walk (SAW) on $\mathbb{Z}^d$ for $d\geq5$ and use it to prove pattern theorems for the self-avoiding walk. We show that infinite two-sided SAW is the infinite-shift limit of infinite…
We have analyzed geometric and topological features of self-avoiding walks. We introduce a new kind of walk: the loop-deleted self-avoiding walk (LDSAW) motivated by the interaction of chromatin with the nuclear lamina. Its critical…
We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability…
The scaling behavior of self-avoiding walks (SAWs) on the backbone of percolation clusters in two, three and four dimensions is studied by Monte Carlo simulations. We apply the pruned-enriched Rosenbluth chain-growth method (PERM). Our…
In this paper, we study the scaling limit of a class of random walks which behave like simple random walks outside of a bounded region around the origin and which are subject to a partial reflection near the origin. If the probability of…
We show that if the three dimensional self-avoiding walk (SAW) is conformally invariant, then one can compute the hitting densities for the SAW in a half space and in a sphere. We test these predictions by Monte Carlo simulations and find…
This article presents SAWdoubler, a package for counting the total number Z(N) of self-avoiding walks (SAWs) on a regular lattice by the length-doubling method, of which the basic concept has been published previously by us. We discuss an…