Electronic Journal of Probability http://ejp.ejpecp.org/ <p><strong> </strong></p>The <strong>Electronic Journal of Probability</strong> (EJP) publishes full-length research articles in probability theory. Short papers, those less than 12 pages, should be submitted first to its sister journal, the <a href="http://ecp.ejpecp.org/" target="_blank">Electronic Communications in Probability</a> (ECP). EJP and ECP share the same editorial board, but with different Editors in Chief.<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> en-US The 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. Applying this standard license to your work will ensure your right to make your work freely and openly available.<br /><br /><strong>Summary of the Creative Commons Attribution License</strong><br /><br />You are free<br /><ul><li> to copy, distribute, display, and perform the work</li><li> to make derivative works</li><li> to make commercial use of the work</li></ul>under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author. ledoux@math.univ-toulouse.fr (Michel Ledoux (Chief Editor)) ejpecp@chafai.net (Djalil Chafaï) Thu, 02 Jan 2014 01:40:36 -0800 OJS http://blogs.law.harvard.edu/tech/rss 60 From sine kernel to Poisson statistics http://ejp.ejpecp.org/article/view/3742 <span>We study the Sine beta</span><span> process introduced in Valko and Virag, when the inverse temperature beta</span><span> tends to </span><span id="MathJax-Element-3-Frame" class="MathJax"><span id="MathJax-Span-9" class="math"><span><span><span id="MathJax-Span-10" class="mrow"><span id="MathJax-Span-11" class="mn">0</span></span></span></span></span></span><span>. This point process has been shown to be the scaling limit of the eigenvalues point process in the bulk of beta</span><span>-ensembles and its law is characterised in terms of the winding numbers of the Brownian carrousel at different angular speeds. After a careful analysis of this family of coupled diffusion processes, we prove that the Sine-beta </span><span>point process converges weakly to a Poisson point process on the real line</span><span>. Thus, the Sine-beta </span><span>point processes establish </span><span style="font-size: 10px;">a smooth crossover between the rigid clock (or picket fence) process (corresponding to </span><span style="font-size: 10px;">$\beta=\infty$</span><span style="font-size: 10px;">) and the </span><span style="font-size: 10px;">Poisson</span><span style="font-size: 10px;"> process.</span> Romain Allez, Laure Dumaz http://ejp.ejpecp.org/article/view/3742 Fri, 12 Dec 2014 12:37:20 -0800 Two particles' repelling random walks on the complete graph http://ejp.ejpecp.org/article/view/2669 We consider two particles' repelling random walks on complete graphs. In this model, each particle has higher probability to visit the vertices which have been seldom visited by the other one. By a dynamical approach we prove that the two particles' occupation measure asymptotically has small joint support almost surely if the repulsion is strong enough. Jun Chen http://ejp.ejpecp.org/article/view/2669 Fri, 12 Dec 2014 10:09:12 -0800 Belief propagation for minimum weight many-to-one matchings in the random complete graph http://ejp.ejpecp.org/article/view/3491 In a complete bipartite graph with vertex sets of cardinalities $n$ and $n^\prime$, assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as $n\rightarrow\infty$, with $n^\prime=\lceil n/\alpha\rceil$ for any fixed $\alpha&gt;1$, the minimum weight of many-to-one matchings converges to a constant (depending on $\alpha$). Many-to-one matching arises as an optimization step in an algorithm for genome sequencing and as a measure of distance between finite sets. We prove that a belief propagation (BP) algorithm converges asymptotically to the optimal solution. We use the objective method of Aldous to prove our results. We build on previous works on minimum weight matching and minimum weight edge cover problems to extend the objective method and to further the applicability of belief propagation to random combinatorial optimization problems. Mustafa Khandwawala http://ejp.ejpecp.org/article/view/3491 Thu, 11 Dec 2014 02:37:48 -0800 Spontaneous breaking of rotational symmetry in the presence of defects http://ejp.ejpecp.org/article/view/2971 We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms. Markus Heydenreich, Franz Merkl, Silke W.W. Rolles http://ejp.ejpecp.org/article/view/2971 Thu, 11 Dec 2014 02:27:30 -0800 On the distances between probability density functions http://ejp.ejpecp.org/article/view/3175 We give estimates of the distance between the densities of the laws of two functionals $F$ and $G$ on the Wiener space in terms of the Malliavin-Sobolev norm of $F-G.$ We actually consider a  more general framework which allows one to treat with similar (Malliavin type)methods functionals of a Poisson point measure (solutions of jump type stochastic equations). We use the above estimates in order to obtain a criterion which ensures that convergence in distribution implies convergence in total variation distance; in particular, if the functionals at hand are absolutely continuous, this implies convergence in $L^{1}$ of the densities. Vlad Bally, Lucia Caramellino http://ejp.ejpecp.org/article/view/3175 Thu, 11 Dec 2014 01:50:20 -0800