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We consider the Cauchy problem for the defocusing cubic NLS on R3T1 and establish almost sure scattering for random initial data. The main obstacle to extend the classical almost sure scattering resul...
We give an explicit AE-axiomatization of the almost sure theories of sparse random graphs G(n, n−α) of Shelah-Spencer. In the process we give a method of constructing extensions of graphs whos...
Independence screening is a powerful method for variable selection for `Big Data' when the number of variables is massive. Commonly used independence screening methods are based on marginal correlatio...
Fine regularity of stochastic processes is usually measured in a local way by local H\"older exponents and in a global way by fractal dimensions. Following a previous work of Adler, we connect these t...
We prove a new sharp correlation inequality for sums of i.i.d.square integrable lattice distributed random variables. We also apply it to establish an almost sure local limit theorem for iid square in...
Let §N be a M ×N randommatrix defined by §N = BN +σWN where BN is a uniformly bounded deterministicmatrix andwhereWN is an independent identically distributed complex Gaussianmatrix with zeromean and ...
In this work, we present results of Almost Sure Convergence and in Quadratic Mean of the gradient stochastic process for the sequential estimation of a conditional expectation. This work is motived b...
In this paper, we prove that the process of product variation of a two-parameter smooth martingale admits an $\infty$ modification, which can be constructed as the quasi-sure limit of sum of the corre...
In this paper we prove the almost sure convergence of the stable tail empirical dependence function for multivariate extreme values.

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