Self-avoiding walk
View article
Random walk on random walks Open
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\\rho \\in (0,\\infty)…
View article
Random-Length Random Walks and Finite-Size Scaling in High Dimensions Open
We address a long-standing debate regarding the finite-size scaling (FSS) of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rigorously. We prove that this model exhibits the same u…
View article
Fast MCMC sampling algorithms on polytopes Open
We propose and analyze two new MCMC sampling algorithms, the Vaidya walk and the John walk, for generating samples from the uniform distribution over a polytope. Both random walks are sampling algorithms derived from interior point methods…
View article
Relation between random walks and quantum walks Open
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the…
View article
Localization of directed polymers with general reference walk Open
Directed polymers in random environment have usually been constructed with a simple random walk on the integer lattice. It has been observed before that several standard results for this model continue to hold for a more general reference …
View article
Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice Open
A two-dimensional discrete-time quantum walk (DTQW) can be realized by\nalternating a two-state DTQW in one spatial dimension followed by an evolution\nin the other dimension. This was shown to reproduce a probability distribution\nfor a c…
View article
Three-dimensional terminally attached self-avoiding walks and bridges Open
We study terminally attached self-avoiding walks (SAWs) and bridges on the simple cubic lattice, both by series analysis and Monte Carlo methods. We provide strong numerical evidence supporting a scaling relation between SAWs, bridges, and…
View article
Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices Open
Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-…
View article
The inner boundary of random walk range Open
In this paper, we deal with the inner boundary of random walk range, that is, the set of those points in a random walk range which have at least one neighbor site outside the range. If $L_n$ be the number of the inner boundary points of ra…
View article
Globule-coil transition in the dynamic HP model Open
We consider a dynamic version of the HP model of a linear polymer: a self-avoiding walk on the square lattice, with monomers being either hydrophobic (H) or polar (P). We simulate the model in two dimensions in the grand canonical assemble…
View article
Weakly self-avoiding walk on a high-dimensional torus Open
How long does a self-avoiding walk on a discrete $d$-dimensional torus have\nto be before it begins to behave differently from a self-avoiding walk on\n$\\mathbb{Z}^d$? We consider a version of this question for weakly self-avoiding\nwalk …
View article
Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices Open
Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-…
View article
Self-avoiding walk on a square lattice with correlated vacancies Open
The self-avoiding walk on the square site-diluted correlated percolation lattice is considered. The Ising model is employed to realize the spatial correlations of the metric space. As a well-accepted result, the (generalized) Flory's mean-…
View article
Asymmetric random walks with bias generated by discrete-time counting\n processes Open
We introduce a new class of asymmetric random walks on the one-dimensional\ninfinite lattice. In this walk the direction of the jumps (positive or\nnegative) is determined by a discrete-time renewal process which is independent\nof the jum…
View article
Mean-field tricritical polymers Open
We provide an introductory account of a tricritical phase diagram, in the\nsetting of a mean-field random walk model of a polymer density transition, and\nclarify the nature of the density transition in this context. We consider a\ncontinu…
View article
Two-sided prudent walks: a solvable non-directed model of polymer adsorption Open
Prudent walks are self-avoiding walks which cannot step towards an already\noccupied vertex. We introduce a new model of adsorbing prudent walks on the\nsquare lattice, which start on an impenetrable surface and accrue a fugacity\n$a$ with…
View article
Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs Open
We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The c…
View article
The random walk penalised by its range in dimensions $d\geq 3$ Open
We study a self-attractive random walk such that each trajectory of length $N$ is penalised by a factor proportional to $\exp ( - |R_N|)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close …
View article
Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model Open
The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface…
View article
Exact Propagators of One-Dimensional Self-Interacting Random Walks Open
Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time t with the territory already visited at earlier times t^{'}<t. This class of non-Markovian random walks has …
View article
Scaling limit of the uniform prudent walk Open
We study the 2-dimensional uniform prudent self-avoiding walk, which assigns equal probability to all nearest-neighbor self-avoiding paths of a fixed length that respect the prudent condition, namely, the path cannot take any step in the d…
View article
Exact Enumeration Approach to Estimate the Theta Temperature of Interacting Self-Avoiding Walks on the Simple Cubic Lattice Open
We compute the exact root-mean-square end-to-end distance of the interacting self-avoiding walk (ISAW) up to 27 steps on the simple cubic lattice. These data are used to construct a fixed point equation to estimate the theta temperature of…
View article
Connective constant for a weighted self-avoiding walk on $\mathbb{Z}^2$ Open
We consider a self-avoiding walk on the dual $\\mathbb{Z}^2$ lattice.This walk can\ntraverse the same square twice but cannot cross the same edge more than once. The weight\nof each square visited by the walk depends on the way the walk pa…
View article
A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpiński gasket Open
We show that the 'erasing-larger-loops-first' (ELLF) method, which was first introduced for erasing loops from the simple random walk on the Sierpiński gasket, does work also for non-Markov random walks, in particular, self-repelling walks…
View article
Two-point functions of random-length random walk on high-dimensional boxes Open
We study the two-point functions of a general class of random-length random walks on finite boxes in $\ZZ^d$ with $d\ge3$, and provide precise asymptotics for their behaviour. We show that the finite-box two-point function is asymptotic to…
View article
Self-avoiding walk on nonunimodular transitive graphs Open
We study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the bubble diagram converges at criticality, and that the critical two-point functi…
View article
On properties of non-markovian random walk in one dimension Open
We study a strongly Non-Markovian variant of random walk in which the probability of visiting a given site i is a function f of number of previous visits v(i) to the site. If the probability is inversely proportional to number of visits to…
View article
Collapse transition of short polymers on simple cubic lattice Open
Denatured proteins and polymers exhibit two types of conformations in solution. Extended coil conformation and compact globule conformation. There is a phase transition associated with these conformation change as a function of temperature…
View article
Quantum ultra-walks: Walks on a line with hierarchical spatial heterogeneity Open
We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which t…
View article
Scaling limit of a self-avoiding walk interacting with spatial random permutations Open
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 s…