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We consider dynamic random walks where the nearest neighbour jump rates are determined by an underlying supercritical contact process in equilibrium. This has previously been studied by den Hollander and dos Santos and den Hollander, dos Santos, Sidoravicius. We show the CLT for such a random walk, valid for all supercritical infection rates for the contact process environment.
In this paper we prove that, under the assumption of quasi-transitivity, if a branching random walk on ${{mathbb{Z}}^d}$ survives locally (at arbitrarily large times there are individuals alive at the origin), then so does the same process when restr
In this paper, we are interested in the asymptotic behaviour of the sequence of processes $(W_n(s,t))_{s,tin[0,1]}$ with begin{equation*} W_n(s,t):=sum_{k=1}^{lfloor ntrfloor}big(1_{{xi_{S_k}leq s}}-sbig) end{equation*} where $(xi_x, xinmathbb{Z}^d)$
A classical result for the simple symmetric random walk with $2n$ steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the maximum height all have exactly the same distribution and converge whe
Let $U_1,U_2,ldots$ be random points sampled uniformly and independently from the $d$-dimensional upper half-sphere. We show that, as $ntoinfty$, the $f$-vector of the $(d+1)$-dimensional convex cone $C_n$ generated by $U_1,ldots,U_n$ weakly converge
In this paper, we analyse a sub-class of two-dimensional homogeneous nearest neighbour (simple) random walk restricted on the lattice using the matrix geometric approach. In particular, we first present an alternative approach for the calculation of