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Any of these conditions can be waived by permission of the Corresponding Author. ecp@iam.uni-bonn.de (Anton Bovier (Chief Editor)) ejpecp@chafai.net (Djalil Chafaï) Thu, 09 Jan 2014 00:05:12 -0800 OJS http://blogs.law.harvard.edu/tech/rss 60 The travel time in a finite box in supercritical Bernoulli percolation http://ecp.ejpecp.org/article/view/3015 We consider the standard site percolation model on the three dimensional cubic lattice. Starting solely with the hypothesis that $\theta(p)&gt;0$, we prove that, for any $\alpha&gt;0$, there exists $\kappa&gt;0$ such that, with probability larger than $1-1/n^\alpha$, every pair of sites inside the box $\Lambda(n)$ are joined by a path having at most $\kappa(\ln n)^2$ closed sites. Raphaël Cerf http://ecp.ejpecp.org/article/view/3015 Sat, 12 Apr 2014 03:39:34 -0700 Erratum: A note on Kesten's Choquet-Deny lemma http://ecp.ejpecp.org/article/view/3381 <div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p>This is an erratum for <strong><a href="/article/view/2629" target="_self">ECP volume 18 paper 65 (2013)</a></strong>. In Proposition 3.1, Condition (C) does not imply that the set Λ(Γ) generates a dense subgroup of R. This has to be made an assumption. Alternatively, one can assume that the matrices are invertible.</p></div></div></div> Sebastian Mentemeier http://ecp.ejpecp.org/article/view/3381 Wed, 19 Mar 2014 02:21:29 -0700 Hedging of game options under model uncertainty in discrete time http://ecp.ejpecp.org/article/view/2714 We introduce a setup of model uncertaintyin discrete time. In this setup wederive dual expressions for the super-replication prices of game options with upper semicontinuous payoffs. We show that the super-replication price is equal to the supremum over a special (non dominated) set of martingale measures, of the corresponding Dynkin games values. This type of results is also new for American options. Yan Dolinsky http://ecp.ejpecp.org/article/view/2714 Sun, 16 Mar 2014 04:49:40 -0700 Law of large numbers for critical first-passage percolation on the triangular lattice http://ecp.ejpecp.org/article/view/3268 We study the site version of (independent) first-passage percolation on the triangular lattice $T$.  Denote the passage time of the site $v$ in $T$ by $t(v)$, and assume that $\mathbb{P}(t(v)=0)=\mathbb{P}(t(v)=1)=1/2$.  Denote by $a_{0,n}$ the passage time from 0 to (n,0), and by b_{0,n} the passage time from 0 to the halfplane $\{(x,y) : x\geq n\}$.  We prove that there exists a constant $0&lt;\mu&lt;\infty$ such that as $n\rightarrow\infty$, $a_{0,n}/\log n\rightarrow \mu$ in probability and $b_{0,n}/\log n\rightarrow \mu/2$ almost surely.  This result confirms a prediction of Kesten and Zhang<strong></strong>.  The proof relies on the existence of the full scaling limit of critical site percolation on $T$, established by Camia and Newman. Chang-Long Yao http://ecp.ejpecp.org/article/view/3268 Sat, 15 Mar 2014 05:45:34 -0700 Mixing of the noisy voter model http://ecp.ejpecp.org/article/view/2968 We prove that the noisy voter model mixes extremely fast - in time of O(log(n)) on any graph with n vertices - for arbitrarily small values of the "noise parameter". We then explain why, as a result, this is an example of a spin system that is always in the "high-temperature regime". Harishchandra Ramadas http://ecp.ejpecp.org/article/view/2968 Sat, 08 Mar 2014 01:17:40 -0800