Sampling Matrices From Harish-Chandra-Itzykson-Zuber Densities

APA

(2021). Sampling Matrices From Harish-Chandra-Itzykson-Zuber Densities. The Simons Institute for the Theory of Computing. https://simons.berkeley.edu/talks/sampling-matrices-harish-chandra-itzykson-zuber-densities

MLA

Sampling Matrices From Harish-Chandra-Itzykson-Zuber Densities. The Simons Institute for the Theory of Computing, Nov. 30, 2021, https://simons.berkeley.edu/talks/sampling-matrices-harish-chandra-itzykson-zuber-densities

BibTex

          @misc{ scivideos_18800,
            doi = {},
            url = {https://simons.berkeley.edu/talks/sampling-matrices-harish-chandra-itzykson-zuber-densities},
            author = {},
            keywords = {},
            language = {en},
            title = {Sampling Matrices From Harish-Chandra-Itzykson-Zuber Densities},
            publisher = {The Simons Institute for the Theory of Computing},
            year = {2021},
            month = {nov},
            note = {18800 see, \url{https://scivideos.org/Simons-Institute/18800}}
          }
          
Colin McSwiggen (Courant Institute, New York University)
Source Repository Simons Institute

Abstract

Exponential densities on unitary conjugation orbits of Hermitian matrices, known as Harish-Chandra-Itzykson-Zuber (HCIZ) densities, are important in various settings in physics and random matrix theory. However, the basic question of efficient sampling from these densities has remained open. We present two efficient algorithms to sample matrices from distributions that are close to the HCIZ distribution. Both algorithms exploit a natural self-reducible structure that arises from continuous symmetries of the underlying unitary orbit. We will also discuss applications to quantum inference and differentially private rank-k approximation.