Electronic Communications in Probability 2014-07-26T00:42:52-07:00 Anton Bovier (Chief Editor) Open Journal Systems The Electronic Journal of Probability applies the <a href="" 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="" 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="">Institute of Mathematical Statistics</a> (IMS) and the <a href=""> Bernoulli Society</a>. This web site uses the <a href="">Open Journal System</a> (OJS) free software developed by the non-profit organization <a href="">Public Knowledge Project</a> (PKP).</p><p>Please consider donating to the <a href="" target="_blank">Open Access Fund</a> of the IMS at this <a href="" target="_blank"><strong>page</strong></a> to keep the journal free.</p> Ergodicity of the Airy line ensemble 2014-07-26T00:42:52-07:00 Ivan Corwin Xin Sun <p>In this paper, we establish the ergodicity of the Airy line ensemble with respect to horizontal shifts. This shows that it is the only candidate for Conjecture 3.2 in Corwin &amp; Hammond, Invent. Math. 2014, regarding the classification of ergodic line ensembles satisfying a certain Brownian Gibbs property after a parabolic shift.</p> 2014-07-26T00:42:36-07:00 Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time 2014-07-26T00:42:52-07:00 Jeremy Thane Clark I consider a stochastic optimization problem for a one-dimensional continuous martingale whose diffusion rate is constrained to be between two positive values $r_{1}&lt;r_{2}$. The problem is to find an optimal adapted strategy for the choice of diffusion rate in order to maximize the chance of hitting an infinitesimal region around the origin at a set time in the future. More precisely, the parameter associated with "the chance of hitting the origin" is the exponent for a singularity induced at the origin of the final time probability density. I show that the optimal exponent solves a transcendental equation depending on the ratio $\frac{r_{2}}{r_{1}}$. 2014-07-26T00:31:33-07:00 A spectral decomposition for the block counting process of the Bolthausen-Sznitman coalescent 2014-07-26T00:42:52-07:00 Martin Möhle Helmut Pitters A spectral decomposition for the generator and the transition probabilities of the block counting process of the Bolthausen-Sznitman coalescent is derived. This decomposition is closely related to the Stirling numbers of the first and second kind. The proof is based on generating functions and exploits a certain factorization property of the Bolthausen-Sznitman coalescent. As an application we derive a formula for the hitting probability $h(i,j)$ that the block counting process of the Bolthausen-Sznitman coalescent ever visits state $j$ when started from state $i\ge j$. Moreover, explicit formulas are derived for the moments and the distribution function of the absorption time $\tau_n$ of the Bolthausen-Sznitman coalescent started in a partition with $n$ blocks. We provide an elementary proof for the well known convergence of $\tau_n-\log\log n$ in distribution to the standard Gumbel distribution. It is shown that the speed of this convergence is of order $1/\log n$. 2014-07-23T00:28:50-07:00 Mixing under monotone censoring 2014-07-26T00:42:52-07:00 Jian Ding Elchanan Mossel We initiate the study of mixing times of Markov chain under monotone censoring. Suppose we have some Markov Chain $M$ on a state space $\Omega$ with stationary distribution $\pi$ and a monotone set $A \subset \Omega$. We consider the chain $M'$ which is the same as the chain $M$ started at some $x \in A$ except that moves of $M$ of the form $x \to y$ where $x \in A$ and $y \notin A$ are {\em censored} and replaced by the move $x \to x$. If $M$ is ergodic and $A$ is connected, the new chain converges to $\pi$ conditional on $A$. In this paper we are interested in the mixing time of the chain $M'$ in terms of properties of $M$ and $A$. Our results are based on new connections with the field of property testing. A number of open problems are presented. 2014-07-20T07:54:22-07:00 On differentiability of stochastic flow for а multidimensional SDE with discontinuous drift 2014-07-26T00:42:52-07:00 Olga Aryasova Andrey Pilipenko We consider a <em>d</em>-dimensional SDE with an identity diffusion matrix and a drift vector being a vector function of bounded variation. We give a representation for the derivative of the solution with respect to the initial data. 2014-07-15T02:18:00-07:00