Related papers: Endless self-avoiding walks
We consider lattice self-avoiding walks and discuss the dynamic critical behavior of two dynamics that use local and bilocal moves and generalize the usual reptation dynamics. We determine the integrated and exponential autocorrelation…
The connective constant $\mu(G)$ of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. The relationship between connective constants and amenability is explored in the…
In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha; universal…
This paper introduces nondeterministic walks, a new variant of one-dimensional discrete walks. At each step, a nondeterministic walk draws a random set of steps from a predefined set of sets and explores all possible extensions in parallel.…
We review some recent results obtained in the framework of the 2-dimensional Interacting Self-Avoiding Walk (ISAW). After a brief presentation of the rigorous results that have been obtained so far for ISAW we focus on the Interacting…
We consider spread-out models of the self-avoiding walk and its finite-memory version, known as the memory-$\tau$ walk, which prohibits loops whose length is at most $\tau$, in dimensions $d>4$. The critical point is defined as the radius…
We study the winding angles of random and self-avoiding walks on square and cubic lattices with number of steps $N$ ranging up to $10^7$. We show that the mean square winding angle $\langle\theta^2\rangle$ of random walks converges to the…
Suppose we are given finitely generated groups $\Gamma_1,...,\Gamma_m$ equipped with irreducible random walks. Thereby we assume that the expansions of the corresponding Green functions at their radii of convergence contain only logarithmic…
The wandering exponent $\nu$ for an isotropic polymer is predicted remarkably well by a simple argument due to Flory. By considering oriented polymers living in a one-parameter family of background tangent fields, we are able to relate the…
We prove an asymptotic Edgeworth expansion for the profiles of certain random trees including binary search trees, random recursive trees and plane-oriented random trees, as the size of the tree goes to infinity. All these models can be…
We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed…
Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being…
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…
Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical…
We consider a branching random walk for which the maximum position of a particle in the n'th generation, M_n, has zero speed on the linear scale: M_n/n --> 0 as n --> infinity. We further remove ("kill") any particle whose displacement is…
We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in…
The number of free sites next to the end of a self-avoiding walk is known as the atmosphere. The average atmosphere can be related to the number of configurations. Here we study the distribution of atmospheres as a function of length and…
We prove a sufficient condition for the two-point function of a statistical mechanical model on $\mathbb{Z}^d$, $d > 2$, to be bounded uniformly near a critical point by $|x|^{-(d-2)} \exp [ -c|x| / \xi ]$, where $\xi$ is the correlation…
A global picture of a random particle movement is given by the convex hull of the visited points. We obtained numerically the probability distributions of the volume and surface of the convex hulls of a selection of three types of…
In this article we consider transient random walks on HNN extensions of finitely generated groups. We prove that the rate of escape w.r.t. some generalised word length exists. Moreover, a central limit theorem with respect to the…