### DIMACS Theoretical Computer Science Seminar

Title: A PTAS for Computing the Supremum of Gaussian Processes

Speaker: **Raghu Meka**, DIMACS

Date: Wednesday, January 23, 2013 11:00-12:00pm

Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. Previously, only a constant factor deterministic polynomial time approximation algorithm was known due to the work of Ding, Lee and Peres. This answers an open question of Lee and Ding.

The study of supremum of Gaussian processes is of considerable importance in probability with applications in functional analysis, convex geometry, and in light of the recent work of Ding, Lee and Peres, to random walks on finite graphs. As such our result could be of use elsewhere. In particular, combining with the recent work of Ding, our result yields a PTAS for computing the cover time of bounded degree graphs. Previously, such algorithms were known only for trees.

Along the way, we also give an explicit oblivious linear estimator for semi-norms in Gaussian space with optimal query complexity.

See: http://paul.rutgers.edu/~yixinxu/theory-spring13.html