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作者：Einmahl, U; Kuelbs, J
作者单位：Universite Libre de Bruxelles; University of Wisconsin System; University of Wisconsin Madison
摘要：We identify the possible cluster sets for a general law of the iterated logarithm in the Banach space setting, and show that all the possible limit sets arise as cluster sets for some random vector in an arbitrary separable Banach space. This extends previous results obtained in finite dimensional Euclidean spaces.
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作者：Holroyd, AE; Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：We consider the following problem: given an i.i.d. family of Bernoulli random variables indexed by Z(d), find a random occupied site X is an element of Z(d) such that relative to X, the other random variables are still i.i.d. Bernoulli. Results of Thorisson imply that such an X exists for all d. Liggett proved that for d = 1, there exists an X with tails P(\X\ greater than or equal to t) of order ct(-1/2), but none with finite 1/2th moment. We prove that for general d there exists a solution w...
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作者：Huang, YC; Dudley, RM
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Let F be any distribution function on R, and F-n be the nth empirical distribution function based on variables i.i.d. (F). It is shown that for 2 < p < infinity and a constant C(p) < infinity, not depending on F, on some probability space there exist Fn and Brownian bridges B-n such that for the Wiener-Young p-variation norm parallel to . parallel to([p]), Eparallel ton(1/2)(F-n - F) - B-n o Fparallel to([P]) less than or equal to C(p)n((2-p)/(2p)), where (B-n o F)(x) = B-n(F(x)). The expectat...
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作者：Duvillard, TC; Guionnet, A
作者单位：Universite Paris Cite; Ecole Normale Superieure de Lyon (ENS de LYON)
摘要：Using It (o) over caps calculus, we study the large deviations properties of the law of the spectral measure of the Hermitian Brownian motion. We extend this strategy to the symmetric, unitary and Wishart processes. This dynamical approach is generalized to the study of the large deviations of the non-commutative laws of several independent Hermitian Brownian motions. As a consequence, we can bound from above entropies defined in the spirit of the microstates entropy introduced by Voiculescu.
