Electronic Journal of Probability 2014-12-12T12:39:05-08:00 Michel Ledoux (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></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="" 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="">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> From sine kernel to Poisson statistics 2014-12-12T12:39:05-08:00 Romain Allez Laure Dumaz <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> 2014-12-12T12:37:20-08:00 Two particles' repelling random walks on the complete graph 2014-12-12T12:37:59-08:00 Jun Chen 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. 2014-12-12T10:09:12-08:00 Belief propagation for minimum weight many-to-one matchings in the random complete graph 2014-12-12T12:37:59-08:00 Mustafa Khandwawala 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. 2014-12-11T02:37:48-08:00 Spontaneous breaking of rotational symmetry in the presence of defects 2014-12-12T12:37:59-08:00 Markus Heydenreich Franz Merkl Silke W.W. Rolles 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. 2014-12-11T02:27:30-08:00 On the distances between probability density functions 2014-12-12T12:37:59-08:00 Vlad Bally Lucia Caramellino 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. 2014-12-11T01:50:20-08:00