3,495 research outputs found
Kolmogorov's law of the iterated logarithm for noncommutative martingales
We prove Kolmogorov's law of the iterated logarithm for noncommutative
martingales. The commutative case was due to Stout. The key ingredient is an
exponential inequality proved recently by Junge and the author.Comment: Revise
Noncommutative Bennett and Rosenthal inequalities
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to
the noncommutative setting. In addition we provide an improved version of the
noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and
Pinelis, Utev for commutative random variables. We also present new best
constants in Rosenthal's inequality. Applying these results to random Fourier
projections, we recover and elaborate on fundamental results from compressed
sensing, due to Candes, Romberg and Tao.Comment: Published in at http://dx.doi.org/10.1214/12-AOP771 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Free monotone transport for infinite variables
We extend the free monotone transport theorem of Guionnet and Shlyakhtenko to
the case of infinite variables. As a first application, we provide a criterion
for when mixed -Gaussian algebras are isomorphic to ;
namely, when the structure array of a mixed -Gaussian algebra has
uniformly small entries that decay sufficiently rapidly. Here a mixed
-Gaussian algebra with structure array is
the von Neumann algebra generated by and
are the Fock space representations of the commutation relation
,
- …