# Gaussian

Thursday, April 16, 2015 - 10:30am - 11:20am

Ronen Eldan (University of Washington)

We prove that any non-negative function f on Gaussian space that is not too log-concave (namely, a function satisfying Hess(log(f)) > - C Id) has tails strictly better than those given by Markov's inequality:

P(f > c)

where E[f] denotes the (Gaussian) expectation of f. An immediate

consequence is a positive answer to the Gaussian variant of Talagrand's (1989) question about regularization of L^1 functions under the convolution semigroup.

P(f > c)

where E[f] denotes the (Gaussian) expectation of f. An immediate

consequence is a positive answer to the Gaussian variant of Talagrand's (1989) question about regularization of L^1 functions under the convolution semigroup.

Wednesday, August 4, 2010 - 3:30pm - 4:00pm

Thorkild Hansen (Seknion Inc.)

An exact representation is presented for the field inside a sphere

(the observation sphere) due to primary sources enclosed by a second sphere

(the source sphere). The regions bounded by the two spheres have no common

points. The field of the primary sources is expressed in terms of Gaussian

beams whose branch-cut disks are centered in the source sphere. The

expansion coefficients for the standing spherical waves in the observation

sphere are expressed in terms of the output of Gaussian-beam receivers,

(the observation sphere) due to primary sources enclosed by a second sphere

(the source sphere). The regions bounded by the two spheres have no common

points. The field of the primary sources is expressed in terms of Gaussian

beams whose branch-cut disks are centered in the source sphere. The

expansion coefficients for the standing spherical waves in the observation

sphere are expressed in terms of the output of Gaussian-beam receivers,