Identities for Toeplitz determinants and the convergence of moments for random Young diagrams

Percy Deift

Courant Institute and University of Pennsylvania

April 30,



Recently Baik, Deift and Johansson showed that the number of boxes in the
first row of a random Young diagram of size N behaves statistically as N
becomes large, like the largest eigenvalue of a random matrix. They also
conjectured that, in the large N limit, the number of boxes in the first k
rows should behave like the first k eigenvalues of a random matrix, and in
a later publication they verified this conjecture for the second row. The
full conjecture was proved subsequently, first by Okounkov, and then
independently by Borodin-Okounkov-Olshanski and Johansson. The speaker
will discuss some recent related developments.

Return to Applied Math Colloquium home page