Russell David Lyons (6 September 1957) is an American mathematician, specializing in probability theory on graphs, combinatorics, statistical mechanics, ergodic theory and harmonic analysis. [1]
Lyons graduated with B.A. mathematics in 1979 from Case Western Reserve University, [2] where he became a Putnam Fellow in 1977 and 1978. [3] He received his Ph.D. in 1983 from the University of Michigan with the thesis A Characterization of Measures Whose Fourier-Stieltjes Transforms Vanish at Infinity, which was supervised by Hugh L. Montgomery and Allen Shields. [4] Lyons was a postdoc for the academic years 1983–1985 at the University of Paris-Sud. He was an assistant professor at Stanford University from 1985 to 1990 and an associate professor at Indiana University from 1990 to 1994. At Georgia Tech he was a full professor from 2000 to 2003. At Indiana University he was a professor of mathematics from 1994 to 2014 and is since 2014 the James H. Rudy Professor of Mathematics; there he has also been an adjunct professor of statistics since 2006. [2]
Lyons has held visiting positions in the United States, France, and Israel. [2] In 2012 he was elected a Fellow of the American Mathematical Society. [1] In 2014 he was an invited speaker of the International Congress of Mathematicians (ICM) in Seoul. [5] In 2017 a conference was held in Tel Aviv in honor of his 60th birthday. [6]
In mathematics, loop-erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. It is intimately connected to the uniform spanning tree, a model for a random tree. See also random walk for more general treatment of this topic.
The contact process is a stochastic process used to model population growth on the set of sites of a graph in which occupied sites become vacant at a constant rate, while vacant sites become occupied at a rate proportional to the number of occupied neighboring sites. Therefore, if we denote by the proportionality constant, each site remains occupied for a random time period which is exponentially distributed parameter 1 and places descendants at every vacant neighboring site at times of events of a Poisson process parameter during this period. All processes are independent of one another and of the random period of time sites remains occupied. The contact process can also be interpreted as a model for the spread of an infection by thinking of particles as a bacterium spreading over individuals that are positioned at the sites of , occupied sites correspond to infected individuals, whereas vacant correspond to healthy ones.
Kannan Soundararajan is an Indian-born American mathematician and a professor of mathematics at Stanford University. Before moving to Stanford in 2006, he was a faculty member at University of Michigan, where he had also pursued his undergraduate studies. His main research interest is in analytic number theory, particularly in the subfields of automorphic L-functions, and multiplicative number theory.
Gregory Francis Lawler is an American mathematician working in probability theory and best known for his work since 2000 on the Schramm–Loewner evolution.
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Mikhail (Misha) Lyubich is a mathematician who has made important contributions to the fields of holomorphic dynamics and chaos theory.
Lester Dubins was an American mathematician noted primarily for his research in probability theory. He was a faculty member at the University of California at Berkeley from 1962 through 2004, and in retirement was Professor Emeritus of Mathematics and Statistics.
Richard Alejandro Arratia is a mathematician noted for his work in combinatorics and probability theory.
First passage percolation is a mathematical method used to describe the paths reachable in a random medium within a given amount of time.
Gérard Ben Arous is a French mathematician, specializing in stochastic analysis and its applications to mathematical physics. He served as the director of the Courant Institute of Mathematical Sciences at New York University from 2011 to 2016.
Gady Kozma is an Israeli mathematician. Kozma obtained his PhD in 2001 at the University of Tel Aviv with Alexander Olevskii. He is a scientist at the Weizmann Institute. In 2005, he demonstrated the existence of the scaling limit value of the loop-erased random walk in three dimensions and its invariance under rotations and dilations.
The Gaussian correlation inequality (GCI), formerly known as the Gaussian correlation conjecture (GCC), is a mathematical theorem in the fields of mathematical statistics and convex geometry.
Ofer Zeitouni is an Israeli mathematician, specializing in probability theory.
Amir Dembo is an Israeli-American mathematician, specializing in probability theory. He was elected a member of the National Academy of Sciences in 2022, and of the American Academy of Arts and Sciences in 2023.
Friedrich Götze is a German mathematician, specializing in probability theory, mathematical statistics, and number theory.
François Ledrappier is a French mathematician.
Vladas Sidoravicius was a Lithuanian-Brazilian mathematician, specializing in probability theory.
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Stephen Mitchell Samuels was a statistician and mathematician, known for his work on the secretary problem and for the Samuels Conjecture involving a Chebyshev-type inequality for sums of independent, non-negative random variables.
The bunkbed conjecture is a statement in percolation theory, a branch of mathematics that studies the behavior of connected clusters in a random graph. The conjecture is named after its analogy to a bunk bed structure. It was first posited by Pieter Kasteleyn in 1985. A preprint giving a proposed counterexample to the conjecture was posted on the arXiv in October 2024 by Nikita Gladkov, Igor Pak, and Alexander Zimin.