We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on Zd × Z+. In dimensions d > 6, we obtain bounds on exit times, transition… (More)

We study the Abelian sandpile model on Z. In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on… (More)

We consider a random walk S n = n i=1 X i with i.i.d. X i. We assume that the X i take values in Z d , have bounded support and zero mean. For A ⊂ Z d , A = ∅, we define τ A = inf{n ≥ 0 : S n ∈ A}.… (More)

We use the lace expansion to analyse networks of mutually-avoiding self-avoiding walks, having the topology of a graph. The networks are defined in terms of spread-out self-avoiding walks that are… (More)

We study the Abelian sandpile model on Z. In d ≥ 5 we prove existence of the infinite volume addition operator, almost surely w.r.t the infinite volume limit μ of the uniform measures on recurrent… (More)

We study the following problem for critical site percolation on the triangular lattice. Let A and B be sites on a horizontal line e separated by distance n. Consider, in the half-plane above e, the… (More)

Sieving is essential in different number theoretical algorithms. Sieving with large primes violates locality of memory access, thus degrading performance. Our suggestion on how to tackle this problem… (More)

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of… (More)

We study the abelian avalanche model, an analogue of the abelian sandpile model with continuous heights, which allows for arbitrary small values of dissipation. We prove that for non-zero… (More)