Electronic Communications in Probability 2014-12-11T02:00:16-08:00 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. 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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 Note on the $S_2(\delta)$ Distribution and the Riemann Xi Function 2014-12-11T02:00:16-08:00 Dmitry Ostrovsky The theory of $S_2(\delta)$ family of probability distributions is used to give a derivation of the functional equation of the Riemann xi function. The $\delta$ deformation of the xi function is formulated in terms of the $S_2(\delta)$ distribution and shown to satisfy Riemann's functional equation.  Criteria for simplicity of roots of the xi function and for its simple roots to satisfy the Riemann hypothesis are formulated in terms of a differentiability property of the $S_2(\delta)$ family. For application, the values of the Riemann zeta function at the integers and of the Riemann xi function in the complex plane are represented as integrals involving the Laplace transform of $S_2.$ 2014-12-11T01:59:56-08:00 On the range of subordinators 2014-12-11T02:00:16-08:00 Mladen Svetoslavov Savov In this note we look into detail into the box-counting dimension of subordinators. Given that X is a non-decreasing Levy process which is not Compound Poisson process we show that in the limit, a.s., the minimum number of boxes of size $a$ that cover the range of $(X_s)_{s\leq t}$ is a.s. of order $t/U(a)$, where U is the potential function of X. This is a more rened result than the lower and upper index of the box-counting dimension computed by Jean Bertoin in his 1999 book, which deals with the asymptotic of the number of boxes at logarithmic scale. 2014-12-11T00:50:24-08:00 Lower bounds on the smallest eigenvalue of a sample covariance matrix. 2014-12-11T02:00:16-08:00 Pavel Yaskov We provide tight lower bounds on the smallest eigenvalue of a sample covariance matrix of a centred isotropic random vector under weak or no assumptions on its components. 2014-12-06T07:11:11-08:00 Large gaps asymptotics for the 1-dimensional random Schr¨odinger operator 2014-12-11T02:00:16-08:00 Stephanie S.M. Jacquot We show that in the Schr\"{o}dinger point process, Sch$_\tau$, $\tau&gt;0,$ the probability of having no eigenvalue in a fixed interval of size $\lambda$ is given by <br />\[ <br />\exp\left(-\frac{\lambda^2}{4\tau}+\left(\frac{2}{\tau}-\frac{1}{4}\right)\lambda +o(\lambda)\right), <br />\] <br />as $\lambda\to\infty.$ It is a slightly more precise version than the one given in a previous work. 2014-11-26T10:08:25-08:00 A note on the strong formulation of stochastic control problems with model uncertainty 2014-12-11T02:00:16-08:00 Mihai Sirbu We consider a  Markovian stochastic control problem with  model uncertainty. The controller (intelligent player) observes only the state, and, therefore, uses feedback (closed-loop) strategies.  The adverse player (nature) who does not have a direct interest in the payoff, chooses open-loop controls that parametrize Knightian uncertainty. This creates a two-step optimization  problem (like half of a game) over feedback strategies and open-loop controls. The main result is to show that, under some assumptions, this provides the  same value as the  (half of) the zero-sum symmetric game where the adverse player  also plays feedback strategies and actively tries to minimize the payoff. The value function is independent of the filtration accessible to the adverse player. Aside from the modeling issue, the present note is a technical companion to a previous work. 2014-11-26T10:00:38-08:00