Related papers: Ballistic Phase of Self-Interacting Random Walks
The Tree Builder Random Walk is a special random walk that evolves on trees whose size increases with time, randomly and depending upon the walker. After every s steps of the walker, a random number of vertices are added to the tree and…
We consider d-dimensional random surface models which for d=1 are the standard (tied-down) random walks (considered as a random ``string''). In higher dimensions, the one-dimensional (discrete) time parameter of the random walk is replaced…
We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer $n\ge 3$. Using the exact renormalization group method we have been able to obtain…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
In this note we study dynamical random walks (DRW) with internal states. We consider a particle which performs a dynamical random walk on $\mathbb{Z}$ and whose local dynamics is given by expanding maps. We provide sufficient conditions for…
Activated Random Walk is a system of interacting particles which presents a phase transition and a conjectured phenomenon of self-organized criticality. In this note, we prove that, in dimension 1, in the supercritical case, when a segment…
We introduce a new self-interacting random walk on the integers in a dynamic random environment and show that it converges to a pure diffusion in the scaling limit. We also find a lower bound on the diffusion coefficient in some special…
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance…
Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le…
We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that…
We perform a Monte Carlo study of $N$-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions ($d=2$), or the tip of an impenetrable cone in $d=3$, of sizes ranging up to $N=10^6$ steps. We find that the…
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…
A linear polymer grafted to a hard wall and underneath an AFM tip can be modelled in a lattice as a grafted lattice polymer (or self-avoiding walk) compressed underneath a piston approaching the wall. As the piston approaches the wall the…
The problems considered in the present paper have their roots in two different cultures. The 'true' (or myopic) self-avoiding walk model (TSAW) was introduced in the physics literature by Amit, Parisi and Peliti. This is a nearest neighbor…
A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen…
We study the strong form of the ballistic conjecture for random walks in random environments (RWRE). This conjecture asserts that any RWRE which is directionally transient for a nonempty open set of directions satisfies condition $(T)$…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…
The study of the effect of random impurities on the collapse of a flexible polymer in dilute solution has had recent attention with consideration of semi-stiff interacting self-avoiding walks on the square lattice. In the absence of…
We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical - the discrete-time Polya walk, in which the walker steps at each integer moment of time, and…