These notes are based on lectures that I gave at the Summer School in Mathematical
Analysis at the Instituto de Matem aticas de la Universidad Nacional Aut onoma de M exico …

This paper surveys developments over the last decade in harmonic analysis on Lie groups
relative to a heat kernel measure. These include analogs of the Hermite expansion, the …

Let K be a connected Lie group of compact type and let T*(K) be its cotangent bundle. This
paper considers geometric quantization of T*(K), first using the vertical polarization and then …

We use a variant of the Segal–Bargmann transform to study canonically quantized Yang–
Mills theory on a space-time cylinder with a compact structure group K. The non-existent …

We study the (two-parameter) Segal–Bargmann transform B s, t N on the unitary group UN,
for large N. Acting on matrix-valued functions that are equivariant under the adjoint action of …

This paper studies the empirical laws of eigenvalues and singular values for random
matrices drawn from the heat kernel measures on the unitary groups U _N UN and the …

We consider a family of free multiplicative Brownian motions bs, τ parametrized by a real
variance parameter s and a complex covariance parameter τ. We compute the Brown …

We consider the generalized Segal–Bargmann transform, defined in terms of the heat
operator, for a noncompact symmetric space of the complex type. For radial functions, we …

2 XN where YN is an N× N deterministic Hermitian matrix whose eigenvalue distribution
converges as N→∞ and XN and XN are independent Gaussian unitary ensembles. We also …

The free multiplicative Brownian motion bt is the large-N limit of Brownian motion B t N on
the general linear group GL (N; C). We prove that the Brown measure for bt—which is an …