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-USElectronic Journal of Probability1083-6489The 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.Subdiffusive concentration in first passage percolation
http://ejp.ejpecp.org/article/view/3680
We prove exponential concentration in i.i.d. first-passage percolation in Z^d for all dimensions (greater than 1) and general edge-weights. These results extend work of Benaïm-Rossignol to general distributions.Michael DamronJack HansonPhilippe Sosoe2014-11-172014-11-1719Random stable looptrees
http://ejp.ejpecp.org/article/view/2732
We introduce a class of random compact metric spaces $\mathscr{L}_{\alpha}$ indexed by $\alpha~\in(1,2)$ and which we call stable looptrees. They are made of a collection of random loops glued together along a tree structure, and can be informally be viewed as dual graphs of $\alpha$-stable Lévy trees. We study their properties and prove in particular that the Hausdorff dimension of $ \mathscr{L}_{\alpha}$ is almost surely equal to $\alpha$. We also show that stable looptrees are universal scaling limits, for the Gromov-Hausdorff topology, of various combinatorial models. In a companion paper, we prove that the stable looptree of parameter $ \frac{3}{2}$ is the scaling limit of cluster boundaries in critical site-percolation on large random triangulations.Nicolas CurienIgor Kortchemski2014-11-112014-11-1119The approach of Otto-Reznikoff revisited
http://ejp.ejpecp.org/article/view/3418
In this article we consider a lattice system of unbounded continuous spins. Otto and Reznikoff used the two-scale approach to show that exponential decay of correlations yields a logarithmic Sobolev inequality (LSI) with uniform constant in the system size. We improve their statement by weakening the assumptions, for which a more detailed analysis based on two new ingredients is needed. The two new ingredients are a covariance estimate and a uniform moment estimate. We additionally provide a comparison principle for covariances showing that the correlations of a conditioned Gibbs measure are controlled by the correlations of the original Gibbs measure with ferromagnetic interaction. This comparison principle simplifies the verification of the hypotheses of the main result. As an application of the main result we show how sufficient algebraic decay of correlations yields the uniqueness of the infinite-volume Gibbs measure, generalizing a result of Yoshida from finite-range to infinite-range interaction.Georg Menz2014-11-062014-11-0619Walking within growing domains: recurrence versus transience
http://ejp.ejpecp.org/article/view/3272
For normally reflected Brownian motion and for simple random walk on independently growing in time $d$-dimensional domains, $d\ge3$, we establish a sharp criterion for recurrence versus transience in terms of the growth rate.Amir DemboRuojun HuangVladas Sidoravicius2014-11-062014-11-0619Discrepancy estimates for variance bounding Markov chain quasi-Monte Carlo
http://ejp.ejpecp.org/article/view/3132
Markov chain Monte Carlo (MCMC) simulations are modeled as driven by true random numbers. We consider variance bounding Markov chains driven by a deterministic sequence of numbers. The star-discrepancy provides a measure of efficiency of such Markov chain quasi-Monte Carlo methods. We define a pull-back discrepancy of the driver sequence and state a close relation to the star-discrepancy of the Markov chain-quasi Monte Carlo samples. We prove that there exists a deterministic driver sequence such that the discrepancies decrease almost with the Monte Carlo rate $n^{-1/2}$. As for MCMC simulations, a burn-in period can also be taken into account for Markov chain quasi-Monte Carlo to reduce the influence of the initial state. In particular, our discrepancy bound leads to an estimate of the error for the computation of expectations. To illustrate our theory we provide an example for the Metropolis algorithm based on a ball walk. Furthermore, under additional assumptions we prove the existence of a driver sequence such that the discrepancy of the corresponding deterministic Markov chain sample decreases with order $n^{-1+\delta}$ for every $\delta>0$.Josef DickDaniel Rudolf2014-11-052014-11-0519