http://ecp.ejpecp.org/issue/feed Electronic Communications in Probability 2014-10-10T02:49:42-07:00 Anton Bovier (Chief Editor) ecp@iam.uni-bonn.de Open Journal Systems 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. 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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/3848 Erratum: Transience and recurrence of rotor-router walks on directed covers of graphs 2014-10-10T02:49:42-07:00 Ecaterina Sava-Huss sava-huss@tugraz.at Wilfried Huss huss@math.tugraz.at In the paper "Transience and recurrence of rotor-router walks on directed covers of graphs", published in <a href="http://dx.doi.org/10.1214/ECP.v17-2096">ECP volume 17 (2012), no. 41</a> there is an error in the proof of Corollary 3.8. This corollary is essential for the transient part in the proof of Theorem 3.5(b). We fix this error by constructing a new rotor-router process, which fulfills our needs, and for which the statement of Corollary 3.8. holds. 2014-10-10T02:49:16-07:00 http://ecp.ejpecp.org/article/view/3587 Conditional persistence of Gaussian random walks 2014-10-10T02:49:42-07:00 Fuchang Gao fuchang@uidaho.edu Zhenxia Liu zhenxia.liu@hotmail.com Xiangfeng Yang xiangfeng.yang@liu.se Let $\{X_n\}_{n\geq1}$ be a sequence of i.i.d. standard Gaussian random variables, let $S_n=\sum_{i=1}^nX_i$ be the Gaussian random walk, and let $T_n=\sum_{i=1}^nS_i$ be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence:$$\mathbb{P}\left\{\max_{1\leq k \leq n}T_{k} \leq 0\,\,\Big|\,\,T_n=0,S_n=0\right\}\lesssim n^{-1/2},\ \mathbb{P}\left\{\max_{1\leq k \leq 2n}T_{k} \leq 0\,\,\Big|\,\,T_{2n}=0,S_{2n}=0\right\}\gtrsim\frac{n^{-1/2}}{\log n},$$for $n\rightarrow\infty,$ which partially proves a conjecture by Caravenna and Deuschel (2008). 2014-10-10T02:39:56-07:00 http://ecp.ejpecp.org/article/view/3325 A renewal version of the Sanov theorem 2014-10-10T02:49:42-07:00 Mauro Mariani mariani@mat.uniroma1.it Lorenzo Zambotti lorenzo.zambotti@upmc.fr Large deviations for the local time of a process <span>X(</span><span>t) </span><span>are investigated, where X(t)=xi for t∈[Si-1,Si[ and (x_j) are i.i.d. random variables on a Polish space, S_j is the j-th arrival time of a renewal process depending on (x_j). No moment conditions are assumed on the arrival times of the renewal process.</span> 2014-10-08T23:42:03-07:00 http://ecp.ejpecp.org/article/view/3622 A characterization of the Poisson process revisited 2014-10-10T02:49:42-07:00 Benjamin Nehring benjamin.nehring@gmail.com We show that the splitting-characterization of the Poisson point process is an immediate consequence of the Mecke-formula.<br /><br /><br /><br /> 2014-10-03T00:49:07-07:00 http://ecp.ejpecp.org/article/view/3094 A generalized Pólya's urn with graph based interactions: convergence at linearity 2014-10-10T02:49:42-07:00 Jun Chen jchen3@caltech.edu Cyrille Lucas lucas@math.univ-paris-diderot.fr <p>We consider a special case of the generalized Pólya's urn model. Given a finite connected graph $G$, place a bin at each vertex. Two bins are called a pair if they share an edge of $G$. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls. <span style="font-size: 10px;">A question of essential interest for the model is to understand the limiting behavior of the proportion of balls in the bins for different graphs $G$. In this paper, we present two results regarding this question. If $G$ is not balanced-bipartite, we prove that the proportion of balls converges to some deterministic point $v=v(G)$ almost surely. If $G$ is regular bipartite, we prove that the proportion of balls converges to a point in some explicit interval almost surely. </span><span style="font-size: 10px;">The question of convergence remains open in the case when $G$ is non-regular balanced-bipartite.</span></p> 2014-10-03T00:42:20-07:00