In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, where the index of the sequence often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
Wendelin Werner is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal "for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory". He is currently Rouse Ball professor of Mathematics at the University of Cambridge.
In probability theory, the Schramm–Loewner evolution with parameter κ, also known as stochastic Loewner evolution (SLEκ), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensional lattice models in statistical mechanics. Given a parameter κ and a domain in the complex plane U, it gives a family of random curves in U, with κ controlling how much the curve turns. There are two main variants of SLE, chordal SLE which gives a family of random curves from two fixed boundary points, and radial SLE, which gives a family of random curves from a fixed boundary point to a fixed interior point. These curves are defined to satisfy conformal invariance and a domain Markov property.
In probability theory and statistical mechanics, the Gaussian free field (GFF) is a Gaussian random field, a central model of random surfaces.
Oded Schramm was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory.
Jean-François Le Gall is a French mathematician working in areas of probability theory such as Brownian motion, Lévy processes, superprocesses and their connections with partial differential equations, the Brownian snake, random trees, branching processes, stochastic coalescence and random planar maps. He received his Ph.D. in 1982 from Pierre and Marie Curie University under the supervision of Marc Yor. He is currently professor at the University of Paris-Sud in Orsay and is a senior member of the Institut universitaire de France. He was elected to French academy of sciences, December 2013.
Gregory Francis Lawler is an American mathematician working in probability theory and best known for his work since 2000 on the Schramm–Loewner evolution.
Bálint Tόth is a Hungarian mathematician whose work concerns probability theory, stochastic process and probabilistic aspects of mathematical physics. He obtained PhD in 1988 from the Hungarian Academy of Sciences, worked as senior researcher at the Institute of Mathematics of the HAS and as professor of mathematics at TU Budapest. He holds the Chair of Probability at the University of Bristol and is a research professor at the Alfréd Rényi Institute of Mathematics, Budapest.
Jean-Michel Bismut is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.
Sourav Chatterjee is an Indian mathematician, specializing in mathematical statistics and probability theory. Chatterjee is credited with work on the study of fluctuations in random structures, concentration and super-concentration inequalities, Poisson and other non-normal limits, first-passage percolation, Stein's method and spin glasses. He has received a Sloan Fellowship in mathematics, Tweedie Award, Rollo Davidson Prize, Doeblin Prize, Loève Prize, and Infosys Prize in mathematical sciences. He was an invited speaker at the International Congress of Mathematicians in 2014.
A conformal loop ensemble (CLEκ) is a random collection of non-crossing loops in a simply connected, open subset of the plane. These random collections of loops are indexed by a parameter κ, which may be any real number between 8/3 and 8. CLEκ is a loop version of the Schramm–Loewner evolution: SLEκ is designed to model a single discrete random interface, while CLEκ models a full collection of interfaces.
Scott Sheffield is a professor of mathematics at the Massachusetts Institute of Technology. His primary research field is theoretical probability.
The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013.
Grégory Miermont is a French mathematician working on probability, random trees and random maps.
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.
Nikolai Georgievich Makarov is a Russian mathematician. He is known for his work in complex analysis and its applications to dynamical systems, probability theory and mathematical physics. He is currently the Richard Merkin Distinguished Professor of Mathematics at Caltech, where he has been teaching since 1991.
Stanislav Alexeyevich Molchanov is a Soviet and American mathematician.
Nina Holden is a Norwegian mathematician interested in probability theory and stochastic processes, including graphons, random planar maps, the Schramm–Loewner evolution, and their applications to quantum gravity. She is a Junior Fellow at the Institute for Theoretical Studies at ETH Zurich, and has accepted a position as an associate professor at the Courant Institute of Mathematical Sciences of New York University beginning in 2021.
