Related papers: Path decompositions for Markov chains
The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…
We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP-divisibility of the map, i.e., appearance of a…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
The conventional Brownian motion in harmonic systems has provided a deep understanding of a great diversity of dissipative phenomena. We address a rather fundamental microscopic description for the (linear) dissipative dynamics of…
We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact…
The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second…
We produce the first example of bounding total variation distance to stationarity and estimating mixing times via orthogonal polynomials diagonalization of discrete reversible Markov chains, the Karlin-McGregor approach.
The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…
We consider Markov chain with spectral gap in $L^2$ space. Assume that $f$ is a bounded function. Then the probabilities of large deviations of average along trajectory satisfy Hoeffding's-type inequalities. These bounds depend only on the…
In this Letter we propose two path integral approaches to describe the classical mechanics of spinning particles. We show how these formulations can be derived from the associated quantum ones via a sort of geometrical dequantization…
Consider a sequence (indexed by n) of Markov chains Z^n in R^d characterized by transition kernels that approximately (in n) depend only on the rescaled state n^{-1} Z^n. Subject to a smoothness condition, such a family can be closely…
We find that Markov chains with finite state space are Poincare chaotic. Moreover, finite realizations of the chains are arcs of each unpredictable orbit for sure. An illustrating example with a proper numerical simulation is provided.
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
The rotor walk is a derandomized version of the random walk on a graph. On successive visits to any given vertex, the walker is routed to each of the neighboring vertices in some fixed cyclic order, rather than to a random sequence of…
The usual random walk on a group (homogeneous both in time and in space) is determined by a probability measure on the group. In a random walk with random transition probabilities this single measure is replaced with a stationary sequence…
We introduce a new Markov Chain called the Cycle Walk for sampling measures of graph partitions where the partition elements have roughly equal size. Such Markov Chains are of current interest in the generation and evaluation of political…
We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
We calculate the large deviation functions characterizing the long-time fluctuations of the occupation of drifted Brownian motion and show that these functions have non-analytic points. This provides the first example of dynamical phase…
For a random walk killed at leaving a cone we suggest two new constructions of a positive harmonic function. These constructions allow one to remove a quite strong extendability assumption, which has been imposed in our previous paper…