# Random

Saturday, October 24, 2015 - 1:45pm - 2:25pm

David Kinderlehrer (Carnegie-Mellon University)

Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. The recently discovered grain boundary character distribution (GBCD) is an empirical distribution of the relative length (in 2D) or area (in 3D) of interface with a given lattice misorientation and normal.

Thursday, October 2, 2014 - 10:15am - 11:05am

Terence Tao (University of California, Los Angeles)

Tuesday, September 30, 2014 - 11:30am - 12:20pm

Terence Tao (University of California, Los Angeles)

Wednesday, October 1, 2014 - 10:15am - 11:05am

Terence Tao (University of California, Los Angeles)

Monday, September 29, 2014 - 9:00am - 9:50am

Terence Tao (University of California, Los Angeles)

Littlewood-Offord theory is the study of random signed sums

of n integers (or more generally, vectors), being particularly

concerned with the probability that such a sum equals a fixed value

(such as zero) or lies in a fixed set (such as the unit ball).

Inverse Littlewood-Offord theory starts with some information about

such probabilities (e.g. that a signed sum equals 0 with high

probability) and deduces structural information about the original

spacings (typically, that they are largely contained within a

of n integers (or more generally, vectors), being particularly

concerned with the probability that such a sum equals a fixed value

(such as zero) or lies in a fixed set (such as the unit ball).

Inverse Littlewood-Offord theory starts with some information about

such probabilities (e.g. that a signed sum equals 0 with high

probability) and deduces structural information about the original

spacings (typically, that they are largely contained within a

Friday, September 12, 2014 - 10:15am - 11:05am

Michael Krivelevich (Tel Aviv University)

We establish the existence of the phase transition in site percolation on pseudo-random d-regular graphs. Let G=(V,E) be an (n,d,lambda)-graph, that is, a d-regular graph on n vertices in which all eigenvalues of the adjacency matrix, but the first one, are at most lambda in their absolute values. Form a random subset R of V by putting every vertex v in V into R independently with probability p.

Monday, September 26, 2011 - 2:00pm - 3:00pm

Alfred Hero III (University of Michigan)

Random matrices are measured in many areas of engineering, social science, and natural science. When the rows of the matrix are random samples of a vector of dependent variables the sample correlations between the columns of the matrix specify a correlation graph that can be used to explore the dependency structure.