Related papers: Strong convergence of partial match queries in ran…

We study the random-link matching problem on random regular graphs, alongside with two relaxed versions of the problem, namely the fractional matching and the so-called "loopy" fractional matching. We estimated the asymptotic average…

Consider a discrete-time martingale, and let $V^2$ be its normalized quadratic variation. As $V^2$ approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian…

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…

We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with…

Random walk on the set of irreducible representations of a finite group is investigated. For the symmetric and general linear groups, a sharp convergence rate bound is obtained and a cutoff phenomenon is proved. As related results, an…

We establish the scaling limit of a class of boundary random walks to the full spectrum of Brownian-type processes on the half-line. By solving the associated martingale problem and employing weak convergence techniques, we prove that under…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…

The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search…

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…

We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…

We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…

We consider the following generalization of binary search in sorted arrays to tree domains. In each step of the search, an algorithm is querying a vertex $q$, and as a reply, it receives an answer, which either states that $q$ is the…

Consider a real-valued branching random walk in the boundary case. Using the techniques developed by A\"id\'ekon and Shi [5], we give two integral tests which describe respectively the lower limits for the minimal position and the upper…

We study random unitary channels which reproduce the action of the twirling channel corresponding to the representation of the symmetric groupon an n-fold tensor product. We derive upper andlower bounds on the randomness cost of…

We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…

We use a random matrix model to study chiral symmetry breaking in QCD at finite chemical potential $\mu$. We solve the model and compute the eigenvalue density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails for…

We provide sufficient conditions which ensure that the intrinsic martingale in the supercritical branching random walk converges exponentially fast to its limit. The case of Galton-Watson processes is particularly included so that our…

We consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609--631] in a one-dimensional super-critical branching random walk, and study the additive martingale $(W_n)$. We prove that, upon the…

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent…