A limit theorem for the Riemann zeta-function near the critical line in the complex space
A limited queuing problem with any number of arrivals and departures
A limiting distribution for quicksort
A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients.
A linear programming approach to error bounds for random walks in the quarter-plane
We consider the steady-state behavior of random walks in the quarter-plane, in particular, the expected value of performance measures that are component-wise linear over the state space. Since the stationary distribution of a random walk is in general not readily available we establish upper and lower bounds on performance in terms of another random walk with perturbed transition probabilities, for which the stationary distribution is a geometric product-form. The Markov reward approach as developed...
A Littlewood-Paley-Stein estimate on graphs and groups
We establish the boundedness in spaces, 1 < q ≤ 2, of a “vertical” Littlewood-Paley-Stein operator associated with a reversible random walk on a graph. This result extends to certain non-reversible random walks, including centered random walks on any finitely generated discrete group.
A local convergence theorem for partial sums of stochastic adapted sequences
In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.
A Local Limit Theorem for Attraction to the Standard Normal Law: The Case of Infinitive Variance.
A local limit theorem for directed polymers in random media : the continuous and the discrete case
A local limit theorem for the critical random graph.
A Local Limit Theorem on the Semi-Direct Product of and
A local limit theorem on the semi-direct product of and
A local limit theorem with speed of convergence for euclidean algorithms and diophantine costs
For large N, we consider the ordinary continued fraction of x=p/q with 1≤p≤q≤N, or, equivalently, Euclid’s gcd algorithm for two integers 1≤p≤q≤N, putting the uniform distribution on the set of p and qs. We study the distribution of the total cost of execution of the algorithm for an additive cost function c on the set ℤ+* of possible digits, asymptotically for N→∞. If c is nonlattice and satisfies mild growth conditions, the local limit theorem was proved previously by the second named author....
A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. III. Relative isomorphism of non-ergodic transformations
A local time inequality for martingales
A logarithmic Sobolev form of the Li-Yau parabolic inequality.
We present a finite dimensional version of the logarithmic Sobolev inequality for heat kernel measures of non-negatively curved diffusion operators that contains and improves upon the Li-Yau parabolic inequality. This new inequality is of interest already in Euclidean space for the standard Gaussian measure. The result may also be seen as an extended version of the semigroup commutation properties under curvature conditions. It may be applied to reach optimal Euclidean logarithmic Sobolev inequalities...
A Logic for Reasoning About Qualitative Probability
A log-scale limit theorem for one-dimensional random walks in random environments.
A log-Sobolev type inequality for free entropy of two projections
We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.
A log-type moment result for perpetuities and its application to martingales in supercritical branching random walks.