Todd Kemp


Contact Info

Todd Kemp
Professor, UC San Diego
Department of Mathematics
AP&M 5202
University of California, San Diego
La Jolla, CA 92093-0112

Phone: (858) 534-3985
Fax: (858) 534-5273



I work in probability theory (stochastic analysis, diffusion processes on Lie groups, random matrices, and free probability), mathematical physics (Yang-Mills theory, quantum information theory), and functional analysis (functional inequalities, heat kernel analysis, holomorphic and subharmonic function spaces).

I am the organizer of the UCSD Functional Analysis Seminar (2019-2020). This is a research-level seminar with largely outside speakers. If you are interested in speaking in the seminars, please contact me.

I am a Founding Faculty member of the Halicioğlu Data Science Institute.

I have 3 former PhD students:

  • Natasha Blitvic (PhD, MIT, 2012) works in noncommutative probability and enumeratuve combinatorics. She was a Zorn postdoctoral fellow at Indiana University, and is now Lecturer (tenure-track Assistant Professor) at Lancaster University in the UK.
  • David Zimmermann (PhD, UCSD, 2015) works on log Sobolev inequalities and random matrices. He was a Dickson Instructor at the University of Chicago, and worked as a senior engineer at Raytheon, in Los Angeles.
  • Ching Wei Ho (PhD, UCSD, 2018) works on the Segal-Bargmann transform, free probability, and complex analysis. He is now a Zorn postdoctoral fellow at Indiana University.

I have one current PhD candidate, Alice Chan, entering her fifth year. She works on the Segal-Bargmann transform on high-dimensional Lie groups, random matrix theory, and free probability.

Here is an increasingly out-of-date research statement: Kemp-Research-2016.pdf



  1. Hypercontractivity in non-commutative holomorphic spaces. Commun. Math. Phys. 259 no. 3, 615-637 (2005)    K-CMP-2005.pdf
  2. Strong Haagerup inequalities for free R-diagonal elements. J. Funct. Anal. 251, 141-173 (2007)   [With Roland Speicher]    KS-JFA-2007.pdf
  3. R-diagonal dilation semigroups. Math. Z. 264, 111-136 (2010)    K-MZ-2010.pdf
  4. Hypercontractivity for log-subharmonic functions. J. Funct. Anal. 258, 1785-1805 (2010)   [With Piotr Graczyk and Jean-Jacques Loeb].    GKL-JFA-2010.pdf
  5. Resolvents of R-diagonal operators. Trans. Amer. Math. Soc. 362, 6029-6064 (2010)   [With Uffe Haagerup and Roland Speicher]    HKS-TAMS-2010.pdf
  6. Enumeration of non-crossing pairings on bitstrings. J. Comb. Theory A. 118, 129-151 (2011)   [With Karl Mahlburg, Amarpreet Rattan, and Cliff Smyth]    KMRS-JCTA-2011.pdf
  7. Duality in Segal-Bargmann Spaces. J. Funct. Anal. 261, 1591-1623 (2011)   [With Will Gryc]    GK-JFA-2011.pdf
  8. Wigner Chaos and the Fourth Moment. Ann. Prob. 40, 1577-1635 (2012)   [With Ivan Nourdin, Giovanni Peccati, and Roland Speicher]    KNPS-AoP-2012.pdf
  9. The Large-N Limit of the Segal-Bargmann Transform on U(N). J. Funct. Anal. 265, 2585-2644 (2013)   [With Bruce Driver and Brian Hall] DHK-JFA-2013.pdf
  10. Liberation of Projections. J. Func. Anal. 266, 1988-2052 (2014) [With Benoit Collins] CK-JFA-2014.pdf
  11. On Sharp Constants in Dual Segal-Bargmann L^p Spaces. J. Math. Anal. Appl. 424, 1198-1222 (2015) [With Will Gryc] GK-JMAA-2015.pdf
  12. Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions. Canad. J. Math. 67 (6), 1384-1410 (2015) [With Piotr Graczyk and Jean-Jacques Loeb] GKL-CJM-2015.pdf
  13. The Large-N Limits of Brownian Motions on GL(N). Int. Math. Res. Not. IMRN, no. 13, 4012-4057 (2016) K-BM-GLN.pdf
  14. Heat Kernel Empirical Laws on U(N) and GL(N). J. Theoret. Probab. 30, no. 2, 397-451 (2017) K-Heat-Kernel-Empirical-Laws.pdf
  15. Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane. Commun. Math. Phys. 351 no. 2, 741-774 (2017) [With Bruce Driver and Brian Hall] DHK-MM-plane.pdf
  16. The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces. Comm. Math. Phys. 352, no. 3, 967-978 (2017) [With Bruce Driver, Franck Gabriel, and Brian Hall] DGHK-MM-surfaces.pdf
  17. The Minimum Renyi Entropy Output of a Quantum Channel is Locally Additive. Lett. Math. Phys. 107, no. 6, 1131-1155 (2017) [With Gilad Gour] GK-Renyi.pdf
  18. The Spectral Edge of Unitary Brownian Motion. Probab. Theory Related Fields 170, no. 1-2, 49-93 (2018) [With Benoit Collins and Antoine Dahlqvist] CDK-PTRF-2016.pdf
  19. Most Boson Quantum States are Almost Maximally Entangled. Proc. Am. Math. Soc. 146, no. 12, 5035-5049 (2018) [With Shmuel Friedland] FK-Boson-Entanglement.pdf
  20. Corrigendum to "On Sharp Constants for Dual Segal-Bargmann L^p Spaces". J. Math. Anal. Appl. 475, no. 2, 1992-1995 (2019) [With Will Gryc] GK-JMAA-2019.pdf
  21. Brown Measure Support and the Free Multiplicative Brownian Motion. To appear in Adv. Math. [With Brian Hall] HK-Brown-Measure-Support.pdf
  22. The Complex Time Segal-Bargmann Transform. To appear in J. Funct. Anal. [With Bruce Driver and Brian Hall] DHK-C-Time-SBT.pdf

In Revisisons:

  1. Fluctuations of Brownian Motions on GL(N). [With Guillaume Cébron] CeK-Fluctuations.pdf
  2. Random Matrices with Log-Range Correlations, and Log-Sobolev Inequalities. [With David Zimmermann] KZ-Log-Correlations.pdf


  1. The Brown Measure of the Free Multiplicative Brownian Motion. [With Bruce Driver and Brian Hall] DHK-Brown-Measure.pdf