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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 Ergodicity of the Airy line ensemble http://ecp.ejpecp.org/article/view/3504 <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> Ivan Corwin, Xin Sun http://ecp.ejpecp.org/article/view/3504 Sat, 26 Jul 2014 00:42:36 -0700 Optimizing a variable-rate diffusion to hit an infinitesimal target at a set time http://ecp.ejpecp.org/article/view/2846 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 $\frac{r_{2}}{r_{1}}$. Jeremy Thane Clark http://ecp.ejpecp.org/article/view/2846 Sat, 26 Jul 2014 00:31:33 -0700 A spectral decomposition for the block counting process of the Bolthausen-Sznitman coalescent http://ecp.ejpecp.org/article/view/3464 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 $1/\log n$. Martin Möhle, Helmut Pitters http://ecp.ejpecp.org/article/view/3464 Wed, 23 Jul 2014 00:28:50 -0700 Mixing under monotone censoring http://ecp.ejpecp.org/article/view/3157 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. Jian Ding, Elchanan Mossel http://ecp.ejpecp.org/article/view/3157 Sun, 20 Jul 2014 07:54:22 -0700 On differentiability of stochastic flow for а multidimensional SDE with discontinuous drift http://ecp.ejpecp.org/article/view/2886 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. Olga Aryasova, Andrey Pilipenko http://ecp.ejpecp.org/article/view/2886 Tue, 15 Jul 2014 02:18:00 -0700