Harry Kesten

Harry Kesten
Name	Harry Kesten
Birth date	5 February 1931
Birth place	Hechingen
Death date	29 March 2019
Death place	Brookline, Massachusetts
Citizenship	United States
Fields	Probability theory, Mathematics
Workplaces	Brandeis University, University of Rochester, Vrije Universiteit Amsterdam
Alma mater	University of California, Berkeley
Doctoral advisor	Joseph L. Doob

Harry Kesten (5 February 1931 – 29 March 2019) was a mathematician renowned for fundamental contributions to probability theory, especially the rigorous analysis of random walks, percolation theory, and branching processes. His work connected deep themes across statistical mechanics, ergodic theory, graph theory, and potential theory, influencing generations of probabilists and mathematical physicists at institutions such as Brandeis University and University of California, Berkeley alumni networks.

Early life and education

Kesten was born in Hechingen and emigrated to the United States where he pursued higher education at the University of California, Berkeley. At Berkeley he studied under Joseph L. Doob, receiving his Ph.D. with a dissertation situated in martingale theory and stochastic processes. During his formative years he interacted with contemporaries linked to André Weil-era influences and postwar American mathematics circles including figures associated with Institute for Advanced Study visits and seminars involving Norbert Wiener's legacy.

Academic career and positions

Kesten held faculty positions at several universities, most notably Brandeis University where he spent the bulk of his career and later became Emeritus. Earlier appointments included the University of Rochester and visiting roles at European centers such as Vrije Universiteit Amsterdam and collaborations at the Courant Institute of Mathematical Sciences. He participated in programs at the Mathematical Sciences Research Institute and delivered lectures at venues including International Congress of Mathematicians sessions, forging ties with researchers from Princeton University, Harvard University, Massachusetts Institute of Technology, Cornell University, University of Cambridge, and University of Oxford.

Major contributions and research

Kesten developed seminal results on the behavior of random walks on groups and graphs, producing the influential "Kesten's theorem" relating spectral radius and amenability of groups and thereby connecting to work by John von Neumann, Andrzej Graczynski-style group-theoretic analyses, and later research by Vladimir Kaimanovich and Vershik. He made foundational advances in percolation theory, establishing critical values and uniqueness results for infinite clusters in models studied by Hugo Duminil-Copin, Geoffrey Grimmett, Harry Kesten-named results informed subsequent proofs by Oded Schramm and Stanislav Smirnov. His 1980s results on one-dimensional and higher-dimensional random walks clarified recurrence and transience criteria related to classic problems studied by George Pólya and reinforced by probabilists like William Feller. Kesten advanced understanding of branching processes, connecting to classical work of A. A. Galton and F. Y. Edgeworth-era lineage, and contributed to limit theorems and large deviations as pursued by C. R. Rao and Varadhan.

He proved precise asymptotics for the return probabilities of symmetric random walks and indexed behavior on lattices such as Z^d complementing analyses by Erdős-style combinatorial probabilists. Kesten's work on harmonic functions on groups and the interplay with spectral theory linked to results by Kesten (spectral)-theory contemporaries and influenced operator-theoretic approaches by Reed and Simon and Barry Simon. His percolation scaling relations presaged renormalization program connections to Kenneth Wilson's physics perspective and rigorous results later obtained by Michael Aizenman, Charles Newman, and Günter Last.

Kesten supervised and collaborated with many students and colleagues who advanced topics in stochastic processes, probabilistic combinatorics, and mathematical physics, building networks that included Persi Diaconis, David Aldous, Gregory Lawler, Yuval Peres, and Oded Schramm among broader probabilistic communities.

Awards and honors

Kesten's achievements were recognized with fellowships and prizes from organizations such as the National Science Foundation and invitations to speak at the International Congress of Mathematicians. He was elected a fellow of the American Academy of Arts and Sciences and received honors from the National Academy of Sciences-related bodies and European mathematical societies, and his work earned him lifetime recognition in retrospectives by the American Mathematical Society and citations in memorial volumes alongside figures like Andrei Kolmogorov, Paul Erdős, and Mark Kac.

Selected publications and students

Selected publications include influential papers on spectral radius and amenability, limit theorems for random walks, and key articles in percolation theory published in journals associated with the American Mathematical Society, Annals of Probability, and proceedings of Symposia in Pure Mathematics. Notable monographs and survey contributions appeared in collections from the Institute of Mathematical Statistics and lecture notes for summer schools at the École Normale Supérieure and CIME programs.

Prominent doctoral students and collaborators include Gregory F. Lawler, Yuval Peres, Bálint Tóth, and other researchers who later held positions at institutions such as Microsoft Research, University of British Columbia, University of Chicago, University of California, Los Angeles, and Tel Aviv University.

Category:American mathematicians Category:Probability theorists Category:1931 births Category:2019 deaths