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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost sure scattering for the cubic NLS on R3T1
R3T1 三次NLS 散射 Cauchy问题
2023/5/18
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...
A simpler axiomatization of the Shelah-Spencer almost sure theories
Shelah-Spencer almost sure theories
2015/9/28
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...
Conditional Sure Independence Screening
False selection rate Generalized linear models Sparsity Sure screening Variable selection
2012/6/21
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...
From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields
Gaussian processes Hausdorff dimension (multi)fractional Brownian motion multiparameter processes Holder regularity stationarity
2012/6/19
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...
A sharp correlation inequality with an application to almost sure local limit theorem
Correlation inequality i.i.d. random variables lattice distributed
2011/2/21
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...
Almost sure localization of the eigenvalues in a gaussian information plus noise model. Applications to the spiked models
localization eigenvalues gaussian information plus noise model
2010/12/14
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 ...
Almost sure convergence and in quadratic mean of the gradient stochastic process for the sequential estimation of a conditional expectation
Stochastic approximation Conditional expectation
2010/9/10
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...
Quasi Sure Product Variation of two Parameter Smooth Martingales on the Wiener Space
quasi-sure $\infty$-modification smooth martingale product variation Kolmogorov's criterion
2007/12/12
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...
ALMOST SURE CONVERGENCE OF THE STABLE TAIL EMPIRICAL DEPENDENCE FUNCTION IN MULTIVARIATE EXTREME STATISTICS
Multivariate extreme value s
2007/12/11
In this paper we prove the almost sure convergence of the stable tail empirical dependence function for multivariate extreme values.