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Mark Kac considered a Markov Chain on the n–sphere based on random rotations in randomly chosen coordinate planes. This same walk was used by Hastings on the orthogonal group. We show that the walk ...
Professor Victor Kac received his A.B. in 1965 and his PhD in 1968 from Moscow State University. Ernest Vinberg was his scientific advisor.Professor Kac taught at the Moscow Institute of Electronic Ma...
Sequential and Quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution s...
We compute the mod $p$ cohomology algebra of a family of infinite discrete Kac-Moody groups of rank two defined over finite fields of characteristic different from $p$.
We construct a family of integrable Hamiltonian systems parametrized by pairs of Coxeter elements in the affine Weyl group. Their phase spaces are double Bruhat cells in the corresponding Kac-Moody gr...
We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).
We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by ...
For a split Kac-Moody group G over an ultrametric field K, S. Gaussent and the author defined an ordered affine hovel on which the group acts; it generalizes the Bruhat-Tits building which corresponds...
Abstract: We give two generalizations of Kac's Theorem on representations of quivers. One is to representations of equipped graphs by relations, in the sense of Gelfand and Ponomarev. The other is to ...
Abstract: This paper is devoted to the study of propagation of chaos and mean-field limit for systems of indistinguable particles undergoing collision processes, as formulated by M. Kac (1956) for a s...
Abstract: This article reviews recent work on the Kac master equation and its low dimensional counterpart, the Kac equation.
Abstract: We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affin...
Abstract: The subject of this article is the Kac equation without cutoff. We first show that in the asymptotic of grazing collisions, the Kac equation can be approximated by a Fokker-Planck equation. ...
For each pair of positive integers r, s, there is a so-called Kac representation (r, s) associated with a Yang-Baxter integrable boundary condition in the lattice approach to the logarithmic minimal m...

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