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We prove that with high probability, d+1 random Bernoulli polynomials in d variables of degree n () do not possess a common root. [ABSTRACT FROM PUBLISHER]

We prove a large deviation principle (LDP) for empirical measures of zeros of random polynomials in one variable. By random polynomial, we mean a Gaussian measure on the space N = H0(ℂℙ1, (N)) determined by inner products GN(h, ν) induced by any smooth Hermitian metric h on (1) → ℂℙ1 and a probability measure dν on ℂℙ1 satisfying the weighted Bernstein–Markov inequality. The speed of the LDP is N2, and the rate function is closely related to the weighted energy of probability measures on ℂℙ1, and in particular, its unique minimizer is the weighted equilibrium measure. [ABSTRACT FROM PUBLISHER]

We consider the discrete two-dimensional Gaussian free field on a box of side length $N$, with Dirichlet boundary data, and prove the convergence of the law of the centered maximum of the field.© 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Studies signal-to interference performance of linear multiuser receivers in random environments. Linear receivers for direct-sequence code-division multiple access systems; Performance of the decorrelator; Performance of the minimum mean-square error receiver; Simulations and numerical results.

Suppose that the integers are assigned i.i.d. random variables {ωx} (taking values in the unit interval), which serve as an environment. This environment defines a random walk { X n } (called a RWRE) which, when at x, moves one step to the right with probability ωx, and one step to the left with probability 1- ω x . Solomon (1975) determined the almost-sure asymptotic speed v α (=rate of escape) of a RWRE. Greven and den Hollander (1994) have proved a large deviation principle for X n / n, conditional upon the environment, with deterministic rate function. For certain environment distributions where the drifts 2 ω x -1 can take both positive and negative values, their rate function vanisheson an interval (0, v α). We find the rate of decay on this interval and prove it is a stretched exponential of appropriate exponent, that is the absolute value of the log of the probability that the empirical mean X n / n is smaller than v, v∈ (0, v α), behaves roughly like a fractional power of n. The annealed estimates of Dembo, Peres and Zeitouni (1996) play a crucial role in the proof. We also deal with the case of positive and zero drifts, and prove there a quenched decay of the form . [ABSTRACT FROM AUTHOR]

Suppose that the integers are assigned i.i.d. random variables {ω} (taking values in the unit interval), which serve as an environment. This environment defines a random walk { X} (called a RWRE) which, when at x, moves one step to the right with probability ω, and one step to the left with probability 1-ω. Solomon (1975) determined the almost-sure asymptotic speed (=rate of escape) of a RWRE. For certain environment distributions where the drifts 2ω-1 can take both positive and negative values, we show that the chance of the RWRE deviating below this speed has a polynomial rate of decay, and determine the exponent in this power law; for environments which allow only positive and zero drifts, we show that these large-deviation probabilities decay like exp(− Cn). This differs sharply from the rates derived by Greven and den-Hollander (1994) for large deviation probabilities conditioned on the environment. As a by product we also provide precise tail and moment estimates for the total population size in a Branching Process with Random Environment. [ABSTRACT FROM AUTHOR]

Consider the massless free field on the d-dimensional lattice ℤ, d≧3; that is the centered Gaussian field on with covariances given by the Green function of the simple random walk on ℤ. We show that the probability, that all the spins are positive in a box of volume N, decays exponentially at a rate of order N log N and compute explicitly the corresponding constant in terms of the capacity of the unit cube. The result is extended to a class of transient random walks with transition functions in the domain of the normal and α-stable law. [ABSTRACT FROM AUTHOR]

The purpose of this paper is two fold. First, bounds on the rate of convergence of empirical measures in controlled Markov chains are obtained under some recurrence conditions. These include bounds obtained through large deviations and central limit theorem arguments. These results are then applied to optima! control problems. Bounds on the rate of convergence of the empirical measures that are uniform over different sets of policies are derived, resulting in bounds on the rate of convergence of the costs. Finally, new optimal control problems that involve not only average cost criteria but also measures on the transient behavior of the cost, namely the rate of convergence, are introduced and applied to a problem in telecommunications. The solution to these problems rely on the bounds introduced in previous sections. [ABSTRACT FROM AUTHOR]

Presents a correction on an article about quenched, annealed and functional large deviations for one-dimensional random walk in random environment.

We prove that Ising models on the hypercube with general quadratic interactions satisfy a Poincaré inequality with respect to the natural Dirichlet form corresponding to Glauber dynamics, as soon as the operator norm of the interaction matrix is smaller than 1. The inequality implies a control on the mixing time of the Glauber dynamics. Our techniques rely on a localization procedure which establishes a structural result, stating that Ising measures may be decomposed into a mixture of measures with quadratic potentials of rank one, and provides a framework for proving concentration bounds for high temperature Ising models. [ABSTRACT FROM AUTHOR]