TORNBERN BERGMAN S THUNDERSTORM LECTURES

Lectures

Lectures 2 – 3 : Wigner ’ s semicircle law

As we set up last week, let M n = [X ij ] n i,j=1 be a symmetric n × n matrix with Random entries such that • X i.j = X j,i • X i,j s are iid for all i < j, and X jj are iid for all j with E[X 2 ij ] = 1, E[X i j] = 0 • All moments exists for each entries. We considered the eigenvector of this random matrix; λ 1 ≤ λ 2 ≤ · · · ≤ λ n which turns out to be random elements depending continuously on...

Bergman ' S Integral Operator Method in Inhomogeneous Elasticity

A severe thunderstorm climatology for Australia and associated thunderstorm environments

Bergman Complexes

Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Φ with corresponding oriented matroid MΦ, then B (MΦ) is dual ...