| Problem number and authors |
PS |
| Problem 1: S. Mallat and O. Zeitouni,
"Optimality of the Karhunen-Loeve basis in nonlinear reconstruction".
Slides of an updated presentation for this problem can be found
HERE
|
 |
| Problem 2: Conjecture:
the (centered) Gaussian measure of the intersection
of two
convex, symmetric subsets of Euclidean space is greater or equal than
the product of the measures of the two subsets.
See for a review of the history of this problem and some partial results:
Schechtman, G., Schlumprecht, Th.,
Zinn, J.,
On the Gaussian measure of the intersection.
Ann. Probab. 26 (1998), 346--357.
MATH REVIEWS LINK.
G. Harge
A particular case of correlation inequality for the Gaussian measure.
Ann. Probab. 27 (1999), 1939--1951.
MATH REVIEWS LINK
|
-- |
| Problem(s) 3: RWRE questions, conjectures: 0-1 laws and other problems.
See
for details the review
"Random walks in random environments",
Proceedings ICM 2002, vol III, pp. 117--127.
For recent progress on related large deviations questions, see
Varadhan's article
MATH REVIEWS LINK.
|
-- |