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Any of these conditions can be waived by permission of the Corresponding Author. ledoux@math.univ-toulouse.fr (Michel Ledoux (Chief Editor)) ejpecp@chafai.net (Djalil Chafaï) Fri, 04 Jan 2013 23:07:22 -0800 OJS 2.3.6.0 http://blogs.law.harvard.edu/tech/rss 60 http://ejp.ejpecp.org/article/view/2234 The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed technique are shown for several classes of stochastic processes. In particular, the main theorem is adjusted to the fractional Brownian motion case. New results on the rate of convergence of the wavelet expansions in the space $C([0,T])$ are also presented. Yuriy Kozachenko, Andriy Olenko, Olga Polosmak http://ejp.ejpecp.org/article/view/2234 Thu, 25 Jul 2013 01:09:58 -0700 http://ejp.ejpecp.org/article/view/2403 We establish a central limit theorem  for the number of roots of the equation $X_N(t) =u$ when $X_N(t)$  is a Gaussian trigonometric  polynomial of degree $N$.  The case $u=0$ was studied by Granville and Wigman. We show that  for some size of the considered interval, the asymptotic behavior is different depending on whether  $u$ vanishes or not. Our mains tools are: a) a chaining argument with the stationary Gaussain process  with covariance $\sin(t)/t$, b) the use of Wiener chaos decomposition that explains  some singularities that appear  in the limit when $u \neq 0$. Jean-Marc Azaïs, Jose R. Leon http://ejp.ejpecp.org/article/view/2403 Thu, 18 Jul 2013 00:03:53 -0700 http://ejp.ejpecp.org/article/view/2586 We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a diffusion process at a fixed deterministic date and the second one concerns the law of a stochastic approximation algorithm at a given time-step. Our results notably improve and complete those obtained in [Frikha, Menozzi, 2012]. The key point is to properly quantify the contribution of the diffusion term to the concentration regime. We also derive a general non-asymptotic deviation bound for the difference between a function of the trajectory of a continuous Euler scheme associated to a diffusion process and its mean. Finally, we obtain non-asymptotic bound for stochastic approximation with averaging of trajectories, in particular we prove that averaging a stochastic approximation algorithm with a slow decreasing step sequence gives rise to optimal concentration rate. Max Fathi, Noufel Frikha http://ejp.ejpecp.org/article/view/2586 Sat, 06 Jul 2013 02:53:22 -0700 http://ejp.ejpecp.org/article/view/2720 The inclusion process is a stochastic lattice gas, which is a natural bosonic counterpart of the well-studied exclusion process and has strong connections to models of heat conduction and applications in population genetics. Like the zero-range process, due to attractive interaction between the particles, the inclusion process can exhibit a condensation transition. In this paper we present first rigorous results on the dynamics of the condensate formation for this class of models. We study the symmetric inclusion process on a finite set $S$ with total number of particles $N$ in the regime of strong interaction, i.e. with independent diffusion rate $m=m_N \to 0$. For the case $Nm_N\to\infty$ we show that on the time scale $1/m_N$ condensates emerge from general homogeneous initial conditions, and we precisely characterize their limiting dynamics. In the simplest case of two sites or a fully connected underlying random walk kernel, there is a single condensate hopping over $S$ as a continuous-time random walk. In the non fully connected case several condensates can coexist and exchange mass via intermediate sites in an interesting coarsening process, which consists of a mixture of a diffusive motion and a jump process, until a single condensate is formed. Our result is based on a general two-scale form of the generator, with a fast-scale neutral Wright-Fisher diffusion and a slow-scale deterministic motion. The motion of the condensates is described in terms of the generator of the deterministic motion and the harmonic projection corresponding to the absorbing states of the Wright Fisher diffusion. Stefan Grosskinsky, Frank Redig, Kiamars Vafayi http://ejp.ejpecp.org/article/view/2720 Wed, 26 Jun 2013 23:41:19 -0700 http://ejp.ejpecp.org/article/view/2425 Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the classical Lipschitz assumption of the observables. Our method is general and offers an unified treatment of diffusions and pure-jump Markov processes on unbounded spaces. Aldéric Joulin, Arnaud Guillin http://ejp.ejpecp.org/article/view/2425 Mon, 24 Jun 2013 23:27:35 -0700