http://ecp.ejpecp.org/issue/feedElectronic Communications in Probability2014-08-14T00:16:17-07:00Anton Bovier (Chief Editor)ecp@iam.uni-bonn.deOpen Journal SystemsThe Electronic Journal of Probability applies the <a href="http://creativecommons.org/licenses/by/2.5/legalcode" target="_blank">Creative Commons Attribution License</a> (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. 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Any of these conditions can be waived by permission of the Corresponding Author.<p><strong></strong>The <strong>Electronic Communications in Probability</strong> (ECP) publishes short research articles in probability theory. Its sister journal, the <a href="http://ejp.ejpecp.org/" target="_self">Electronic Journal of Probability</a> (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.</p><p>EJP and ECP are free access official journals of the <a href="http://www.imstat.org/">Institute of Mathematical Statistics</a> (IMS) and the <a href="http://isi.cbs.nl/BS/bshome.htm"> Bernoulli Society</a>. This web site uses the <a href="http://en.wikipedia.org/wiki/Open_Journal_Systems">Open Journal System</a> (OJS) free software developed by the non-profit organization <a href="http://en.wikipedia.org/wiki/Public_Knowledge_Project">Public Knowledge Project</a> (PKP).</p><p>Please consider donating to the <a href="http://www.imstat.org/publications/open.htm" target="_blank">Open Access Fund</a> of the IMS at this <a href="https://secure.imstat.org/secure/orders/donations.asp" target="_blank"><strong>page</strong></a> to keep the journal free.</p>http://ecp.ejpecp.org/article/view/3237A maximal inequality for supermartingales2014-08-14T00:16:17-07:00Bruce Hajekb-hajek@illinois.eduA tight upper bound is given on the distribution of the maximum of a supermartingale. Specifically, it is shown that if $Y$ is a semimartingale with initial value zero and quadratic variation process $[Y,Y]$ such that $Y + [Y,Y]$ is a supermartingale, then the probability the maximum of $Y$ is greater than or equal to a positive constant $a$ is less than or equal to$1/(1+a).$ The proof makes use of the semimartingale calculus and is inspired by dynamic programming.2014-08-14T00:15:55-07:00http://ecp.ejpecp.org/article/view/3314Growing random 3-connected maps or Comment s'enfuir de l'Hexagone2014-08-14T00:16:17-07:00Louigi Addario-Berrylouigi@math.mcgill.caWe use a growth procedure for binary trees due to Luczak and Winkler, a bijection between binary trees and irreducible quadrangulations of the hexagon due to Fusy, Poulalhon and Schaeffer, and the classical angular mapping between quadrangulations and maps, to define a growth procedure for maps. The growth procedure is local, in that every map is obtained from its predecessor by an operation that only modifies vertices lying on a common face with some fixed vertex. As n tends to infinity, the probability that the n'th map in the sequence is 3-connected tends to 2^8/3^6. The sequence of maps has an almost sure limit G, and we show that G is the distributional local limit of large, uniformly random 3-connected graphs.2014-08-12T20:44:38-07:00http://ecp.ejpecp.org/article/view/3208On criteria of disconnectedness of $\Lambda$-Fleming-Viot support2014-08-14T00:16:17-07:00Xiaowen Zhouxiaowen.zhou@concordia.caThe totally disconnectedness of support for super Brownian motion in high dimensions is well known. In this paper, we prove that similar results also hold for $\Lambda$-Fleming-Viot process with Brownian spatial motion provided that the associated $\Lambda$-coalescent does not come down from infinity fast enough. Our proof is another application of the lookdown particle representation for $\Lambda$-Fleming-Viot process. We also discuss the disjointness of independent $\Lambda$-Fleming-Viot supports and ranges in high dimensions. The disconnectedness of the $\Lambda$-Fleming-Viot support remains open in certain low dimensions.2014-08-11T13:02:31-07:00http://ecp.ejpecp.org/article/view/3490Disjoint crossings, positive speed and deviation estimates for first passage percolation2014-08-14T00:16:17-07:00Ghurumuruhan Ganesangganesan82@gmail.comConsider bond percolation on the square lattice \(\mathbb{Z}^2\) where each edge is independently open with probability \(p.\) For some positive constants \(p_0 \in (0,1), \epsilon_1\) and \(\epsilon_2,\) the following holds: if \(p > p_0,\) then with probability at least \(1-\frac{\epsilon_1}{n^{4}}\) there are at least \(\frac{\epsilon_2 n}{\log{n}}\) disjoint open left-right crossings in \(B_n := [0,n]^2\) each having length at most \(2n,\) for all \(n \geq 2.\) Using the proof of the above, we obtain positive speed for first passage percolation with independent and identically distributed edge passage times \(\{t(e_i)\}_i\) satisfying \(\mathbb{E}\left(\log{t(e_1)}\right)^+<\infty;\) namely, \(\limsup_n \frac{T_{pl}(0,n)}{n} \leq Q\) a.s. for some constant \(Q < \infty,\) where \(T_{pl}(0,n)\) denotes the minimum passage time from the point \((0,0)\) to the line \(x=n\) taken over all paths contained in \(B_n.\) Finally, we also obtain deviation corresponding estimates for nonidentical passage times satisfying \(\inf_i\mathbb{P}(t(e_i) = 0) > \frac{1}{2}.\)2014-08-11T12:48:38-07:00http://ecp.ejpecp.org/article/view/2908The probability that planar loop-erased random walk uses a given edge2014-08-14T00:16:17-07:00Gregory Lawlerlawler@math.uchicago.eduWe give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an $n \times n$ square is used in a loop-erased walk connecting opposite sides is of order $n^{-3/4}$. We, in fact, improve the result by showing that this estimate is correct up to multiplicative constants.2014-08-05T06:27:03-07:00