A card shuffling analysis of deformations of the Plancherel measure of the symmetric group.
A class of quasigroups solving a problem of ergodic theory
A pointed quasigroup is said to be semicentral if it is principally isotopic to a group via a permutation on one side and a group automorphism on the other. Convex combinations of permutation matrices given by the one-sided multiplications in a semicentral quasigroup then yield doubly stochastic transition matrices of finite Markov chains in which the entropic behaviour at any time is independent of the initial state.
A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system
In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established....
A combinatorial approach to the conditioning of a single entry in the stationary distribution for a Markov chain.
A combinatorial problem arising in finite Markov chains
A conjecture on a class of matrices
A contractive property in finite state Markov chains
A criterion for transience of multidimensional branching random walk in random environment.
A determinant formula from random walks
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...
A diffusion approximation in the ruin problem for a controlled Markov chain
A gaussian sheet connected to symmetric Markov chains
A Gauss-Kuzmin theorem for the Rosen fractions
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
A generalized Biane process
A graph method for Markov models solving
A hidden Markov model for an inventory system with perishable items.
A Markov chain approach to randomly grown graphs.
A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains.
A matrix with an application to the motion of an absorbing Markov chain. I.
A Measure Concentration Inequality for Contracting Markov Chains.
A method for knowledge integration
With the aid of Markov Chain Monte Carlo methods we can sample even from complex multi-dimensional distributions which cannot be exactly calculated. Thus, an application to the problem of knowledge integration (e. g. in expert systems) is straightforward.