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Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics, from evolutionary biology to computer science, etc.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables. Many stochastic processes can be represented by time series. However, a stochastic process is by nature continuous while a time series is a set of observations indexed by integers. A stochastic process may involve several related random variables.
A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov.
William "Vilim" Feller, born Vilibald Srećko Feller, was a Croatian-American mathematician specializing in probability theory.
In mathematics, a random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as the integers.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis.
In mathematics, the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large-scale behavior of the manifold resembles that of a Euclidean space.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act.
Paul-André Meyer was a French mathematician, who played a major role in the development of the general theory of stochastic processes. He worked at the Institut de Recherche Mathématique (IRMA) in Strasbourg and is known as the founder of the 'Strasbourg school' in stochastic analysis.
In probability theory, the mixing time of a Markov chain is the time until the Markov chain is "close" to its steady state distribution.
Algebraic statistics is the use of algebra to advance statistics. Algebra has been useful for experimental design, parameter estimation, and hypothesis testing.
Toshikazu Sunada is a Japanese mathematician and author of many books and essays on mathematics and mathematical sciences. He is professor emeritus of both Meiji University and Tohoku University. He is also distinguished professor of emeritus at Meiji in recognition of achievement over the course of an academic career. Before he joined Meiji University in 2003, he was professor of mathematics at Nagoya University (1988–1991), at the University of Tokyo (1991–1993), and at Tohoku University (1993–2003). Sunada was involved in the creation of the School of Interdisciplinary Mathematical Sciences at Meiji University and is its first dean (2013–2017). Since 2019, he is President of Mathematics Education Society of Japan.
In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of spatial point processes, hence notions of Palm conditioning, which extend to the more abstract setting of random measures.
Sergio Albeverio is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis, mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.
James Laurie Snell, often cited as J. Laurie Snell, was an American mathematician.
Yuval Peres is a mathematician known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdorff measure, random walks, Brownian motion, percolation and Markov chain mixing times. He was born in Israel and obtained his Ph.D. at the Hebrew University of Jerusalem in 1990 under the supervision of Hillel Furstenberg. He was a faculty member at the Hebrew University and the University of California at Berkeley, and a Principal Researcher at Microsoft Research in Redmond, Washington. Peres has been accused of sexual harassment by several female scientists.
Nicholas Theodore Varopoulos is a Greek mathematician, who works on harmonic analysis and especially analysis on Lie groups.
Yves Le Jan is a French mathematician working in Probability theory and Stochastic processes.
Michel Ledoux is a French mathematician, specializing in probability theory. He is a professor at the University of Toulouse.
Stanislav Alexeyevich Molchanov is a Soviet and American mathematician.
