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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) Thu, 02 Jan 2014 01:40:36 -0800 OJS http://blogs.law.harvard.edu/tech/rss 60 Fluctuation exponents for directed polymers in the intermediate disorder regime http://ejp.ejpecp.org/article/view/3307 We derive exact fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate scaling regime. This regime corresponds to taking the inverse temperature to zero as the size of the system goes to infinity. The exponents satisfy the KPZ scaling relation and coincide with physical predictions.In the critical case, we recover the fluctuation exponent of the Hopf-Cole solution of the KPZ equation in equilibrium and close to equilibrium. Gregorio R. Moreno Flores, Timo Seppäläinen, Benedek Valkó http://ejp.ejpecp.org/article/view/3307 Fri, 26 Sep 2014 00:24:48 -0700 Local probabilities for random walks with negative drift conditioned to stay nonnegative http://ejp.ejpecp.org/article/view/3426 Let $S_n, n=0,1,...,$ with $S_0=0$ be a random walk with negative drift and let $\tau_x=\min\{k&gt;0: S_k&lt;-x\}, \, x\geq 0.$ Assuming that the distribution of i.i.d. increments of the random walk  is absolutely continuous with subexponential density we find the asymptotic behavior, as $n\to\infty$ of the probabilities $\mathbf{P}(\tau_x=n)$ and $\mathbf{P}(S_n\in (y,y+\Delta],\tau_x&gt;n)$ for fixed $x$ and various ranges of $y.$ The case of lattice distribution of increments is considered as well. Denis Denisov, Vladimir Vatutin, Vitali Wachtel http://ejp.ejpecp.org/article/view/3426 Fri, 26 Sep 2014 00:13:31 -0700 A sequential empirical CLT for multiple mixing processes with application to $\mathcal{B}$-geometrically ergodic Markov chains http://ejp.ejpecp.org/article/view/3216 We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions which differs from the class F. This situation occurs in the case of data arising from dynamical systems or Markov chains, for which the Perron-Frobenius or Markov operator, respectively, has a spectral gap on a restricted space. We provide applications to iterative Lipschitz models that contract on average. Herold Dehling, Olivier Durieu, Marco Tusche http://ejp.ejpecp.org/article/view/3216 Sat, 20 Sep 2014 03:20:25 -0700 A Gaussian process approximation for two-color randomly reinforced urns http://ejp.ejpecp.org/article/view/3432 The Polya urn has been extensively studied and is widely applied in many disciplines. An important application  is to use urn models to develop randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed. In this paper, we prove a Gaussian process approximation for the sequence of random composotions of a two-color randomly reinforced urn for both the cases with the equal and unequal reinforcement means. The Gaussian process is a tail stochastic integral with respect to  a Brownian motion. By using the Gaussian approximation, the law of the iterated logarithm and the functional  central limit theorem in both the stable convergence sense and the almost-sure conditional convergence sense are established. Also as a consequence, we are able to prove that the limit distribution of the normalized urn composition has no points masses both  when the reinforcements means are equal and unequal under the assumption of only finite $(2+\epsilon)$-th moments. Lixin Zhang http://ejp.ejpecp.org/article/view/3432 Thu, 18 Sep 2014 02:36:36 -0700 Small deviations for time-changed Brownian motions and applications to second-order chaos http://ejp.ejpecp.org/article/view/2993 We prove strong small deviations results for Brownian motion under independent time-changes satisfying their own asymptotic criteria. We then apply these results to certain stochastic integrals which are elements of second-order homogeneous chaos. Daniel Dobbs, Tai Melcher http://ejp.ejpecp.org/article/view/2993 Tue, 16 Sep 2014 23:38:49 -0700