Related papers: Random walks with different directions: Drunkards …

We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most $n^{1/4 + o_n(1)}$ in $n$ units of time. Together with the complementary lower bound proven by Gwynne and…

The P\'olya number characterizes the recurrence of a random walk. We apply the generalization of this concept to quantum walks [M. \v{S}tefa\v{n}\'ak, I. Jex and T. Kiss, Phys. Rev. Lett. \textbf{100}, 020501 (2008)] which is based on a…

We study models of continuous-time, symmetric, $\Z^{d}$-valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$ with a power law with an exponent $\gamma$ near 0. We…

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no…

The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the…

We give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an n x n square is used in a loop-erased walk connecting opposites sides is of order n^{-3/4}. We, in fact, improve the result by showing that…

We present simulation results for long ($N\leq 4000$) self-avoiding walks in four dimensions. We find definite indications of logarithmic corrections, but the data are poorly described by the asymptotically leading terms. Detailed…

We present a systematic analytical approach to the trapping of a random walk by a finite density rho of diffusing traps in arbitrary dimension d. We confirm the phenomenologically predicted e^{-c_d rho t^{d/2}} time decay of the survival…

Prudent walks are special self-avoiding walks that never take a step towards an already occupied site, and \emph{$k$-sided prudent walks} (with $k=1,2,3,4$) are, in essence, only allowed to grow along $k$ directions. Prudent polygons are…

A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…

We simulate loop-erased random walks on simple (hyper-)cubic lattices of dimensions 2,3, and 4. These simulations were mainly motivated to test recent two loop renormalization group predictions for logarithmic corrections in $d=4$,…

We study the relationship between tournaments and random walks. This connection was first observed by Erd\H{o}s and Moser. Winston and Kleitman came close to showing that $S_n=\Theta(4^n/n^{5/2})$. Building on this, and works by Tak\'acs,…

Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…

We study a natural random walk on the $n \times n$ upper triangular matrices, with entries in $\mathbb{Z}/m \mathbb{Z}$, generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this…

We consider random walks in Dirichlet environment (RWDE) on $\Z ^d$, for $ d \geq 3 $, in the sub-ballistic case. We associate to any parameter $ (\alpha_1, ..., \alpha_{2d}) $ of the Dirichlet law a time-change to accelerate the walk. We…

We consider a one-dimensional random walk among biased i.i.d. conductances, in the case where the random walk is transient but sub-ballistic: this occurs when the conductances have a heavy-tail at $+\infty$ or at $0$. We prove that the…

The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…

We consider random walks on the surface of the sphere $S_{n-1}$ ($n \geq 2$) of the $n$-dimensional Euclidean space $E_n$, in short a hypersphere. By solving the diffusion equation in $S_{n-1}$ we show that the usual law $<r^2 > \varpropto…

This paper proves the formula \nu(d) =1 for d=1 and \nu(d) = max(1/4 +1/d, 1/2) for d > 1 for the root mean square displacement exponent \nu(d) of the self-avoiding walk (SAW) in Z^d, and thus, resolves some major long-standing open…

A connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences. Consequently the scaled distribution of the maximum displacements in a particular asymmeteric version…