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Any of these conditions can be waived by permission of the Corresponding Author. ecp@iam.uni-bonn.de (Anton Bovier (Chief Editor)) ejpecp@chafai.net (Djalil Chafaï) Thu, 09 Jan 2014 00:05:12 -0800 OJS http://blogs.law.harvard.edu/tech/rss 60 A property of Petrov's diffusion http://ecp.ejpecp.org/article/view/3684 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. Stewart N. Ethier http://ecp.ejpecp.org/article/view/3684 Thu, 18 Sep 2014 23:45:50 -0700 Last zero time or maximum time of the winding number of Brownian motions http://ecp.ejpecp.org/article/view/3485 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. Izumi Okada http://ecp.ejpecp.org/article/view/3485 Thu, 18 Sep 2014 03:00:23 -0700 Concentration inequalities for Gibbs sampling under $d_{l_{2}}$-metric http://ecp.ejpecp.org/article/view/3502 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. Neng-Yi Wang http://ecp.ejpecp.org/article/view/3502 Thu, 18 Sep 2014 02:50:33 -0700 A counter example to central limit theorem in Hilbert spaces under a strong mixing condition http://ecp.ejpecp.org/article/view/3249 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. Davide Giraudo, Dalibor Volny http://ecp.ejpecp.org/article/view/3249 Fri, 29 Aug 2014 02:43:32 -0700 A connection of the Brascamp-Lieb inequality with Skorokhod embedding http://ecp.ejpecp.org/article/view/3025 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. Yuu Hariya http://ecp.ejpecp.org/article/view/3025 Fri, 29 Aug 2014 02:35:50 -0700