## Markov Processes and Related Fields, Volume 1 |

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### Contents

Markov Processes | 1 |

Petrova E Scacciatelh | 57 |

Ovseevich The Discrete Laplace Operator in an Oithant | 79 |

Copyright | |

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assume asymptotically compact condition configuration consider constant construct convergence convex Corollary correlation functions corresponding countable countable Markov chains defined definition denote diagrams distribution dual equation ergodic face essential spectrum exists exponentially g-pair Gibbs given Hence holds homogeneous hydrodynamic implies inequality initial interaction Jackson network jumps Large Deviation lattice LD-regular limit theorem limsup Lyapunov functions Markov chain Markov process Math Mathematics matrix Moscow Moscow State University node non-empty non-pole singularity notation obtain paper parameters particle perturbation positive Prob probability measure problem proof of Lemma Proof of Theorem Proposition prove queueing random fields random variables random walks respect RL-function Russia satisfies second vector field Section sequence solution space stationary stochastic string subinvariant subset sufficient Theorem 3.1 theory Toeplitz operators topology transient transition translation invariant unique upper bound V.A. Malyshev vector field vertices voter model zero