Electronic Communications in Probability 2014-09-18T23:46:09-07:00 Anton Bovier (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. 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. <p><strong></strong>The <strong>Electronic Communications in Probability</strong> (ECP) publishes short research articles in probability theory. Its sister journal, the <a href="" 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="">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> A property of Petrov's diffusion 2014-09-18T23:46:09-07:00 Stewart N. Ethier Petrov constructed a diffusion process in the Kingman simplex whose unique stationary distribution is the two-parameter Poisson-Dirichlet distribution of Pitman and Yor.  We show that the subset of the simplex comprising vectors whose coordinates sum to 1 is the natural state space for the process.  In fact, the complementary set acts like an entrance boundary. 2014-09-18T23:45:50-07:00 Last zero time or maximum time of the winding number of Brownian motions 2014-09-18T23:46:09-07:00 Izumi Okada In this paper we consider the winding number, $\theta(s)$, of planar Brownian motion and study asymptotic behavior of the process of the maximum time, the time when $\theta(s)$ attains the maximum in the interval $0\le s \le t$. We find the limit law of its logarithm with a suitable normalization factor and the upper growth rate of the maximum time process itself. We also show that the process of the last zero time of $\theta(s)$ in $[0,t]$ has the same law as the maximum time process. 2014-09-18T03:00:23-07:00 Concentration inequalities for Gibbs sampling under $d_{l_{2}}$-metric 2014-09-18T23:46:09-07:00 Neng-Yi Wang The aim of this paper is to investigate the Gibbs sampling that's used for computing the mean of observables with respect to some function $f$ depending on a very small number of variables. For this type of observable, by using the $d_{l_{2}}$-metric one obtains the sharp concentration estimate for the empirical mean, which in particular yields the correct speed in the concentration for $f$ depending on a single observable. 2014-09-18T02:50:33-07:00 A counter example to central limit theorem in Hilbert spaces under a strong mixing condition 2014-09-18T23:46:09-07:00 Davide Giraudo Dalibor Volny We show that in a separable infinite dimensional Hilbert space, uniform integrability of the square of the norm of normalized partial sums of a strictly stationary sequence, together with a strong mixing condition, does not guarantee the central limit theorem. 2014-08-29T02:43:32-07:00 A connection of the Brascamp-Lieb inequality with Skorokhod embedding 2014-09-18T23:46:09-07:00 Yuu Hariya We reveal a connection of the Brascamp-Lieb inequality with Skorokhod embedding. Error bounds for the inequality in terms of the variance are also provided. 2014-08-29T02:35:50-07:00