Intersections of random walks

By Parkpoom Phetpradap. 2011

397 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d2130f1dfd4f0366b2d147ebbcf58d7b291710fc

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Citations in the corpus

Probability on Trees and Networks (2017, background): “Our proof is from Lyons and Schramm (1999), which also proved the statement about transience. It is also true that for any invariant insertion-tolerant percolation process on a nonamenable quasi-transitive unimodular graph with a unique infinite cluster a.s., that cluster is transient, but this is m”
Marginal triviality of the scaling limits of critical 4D Ising and 𝜑44 models (2019, background): “8)] and [37]), but nevertheless the expected number of points of intersection remains of order Ω(1).”
Topics in Occupation Times and Gaussian Free Fields (2012, unknown): “55) g(x) ∼ cd |x|−(d−2), as x→∞, where cd = 2 (d− 2) |B(0, 1)| = d 2 Γ ( d 2 − 1 ) 1 π d 2 , where |x| stands for the Euclidean norm of x, and |B(0, 1)| for the volume of the unit ball of R (see for instance [15], p.”
Connectivity properties of random interlacement and intersection of random walks (2010, background): “. (2.8) Here, we write H(K) for the ﬁrst entrance time in K, i.e. H(K) = inf{t ≥ 0 : X(t) ∈ K}. We will repeatedly use the following bound on the capacity of B(0,R) in d ≥ 3 (see (2.16) on page 53 in [7]): There exist constants cb = cb(d) > 0 and Cb = Cb(d) < ∞ such that for all positive R, cb”
Gumbel fluctuations for cover times in the discrete torus (2012, background): “42, [12]) and a standard covering argument we have hz(y) ≤ chx(y) for all z ∈ ∂eBk.”
The subleading order of two dimensional cover times (2014, background): “8 [19]), it is concievable that it can also be used to prove (1.”
On the fragmentation of a torus by random walk (2010, methodology): “In particular, using [12], Proposition 1.”
On the size of a finite vacant cluster of random interlacements with small intensity (2010, background): “26) Recall that our definition of cut-times is slightly different from the definition that for instance appears in [5] or [9], p.”