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In this paper, we extend a result of Campanino and Pétritis [Markov Process. Relat. Fields 9 (2003) 391–412].
We study a random walk in with random orientations.
We suppose that the orientation of the kth floor
is given by , where is
a stationary sequence of random variables.
Once the environment fixed, the random walk can go
either up or down or can stay in the present floor (but moving with
respect to its orientation).
This model was introduced by Campanino and Pétritis
in [Markov Process....
Methods based on the theory of Markov chains are most commonly used in the recognition of protein coding sequences. However, they require big learning sets to fill up all elements in transition probability matrices describing dependence between nucleotides in the analyzed sequences. Moreover, gene prediction is strongly influenced by the nucleotide bias measured by e.g. G+C content. In this paper we compare two methods: (i) the classical GeneMark algorithm, which uses a three-periodic non-homogeneous...
Sur un ensemble fini, on s'intéresse aux minorations linéaires
du trou spectral d'un noyau markovien réversible, en terme de
la constante isopérimétrique associée. On montre que la constante
optimale est l'inverse du cardinal de l'ensemble moins un, mais
on verra aussi comment il est possible de l'améliorer dans
certaines situations particulières (arbres pointés radiaux
à nombre fini de générations). Une application des inégalités
précédentes est de retrouver immédiatement le comportement...
Suppose that is a finite, connected graph and is a lazy random walk on . The lamplighter chain associated with is the random walk on the wreath product , the graph whose vertices consist of pairs where is a labeling of the vertices of by elements of and is a vertex in . There is an edge between and in if and only if is adjacent to in and for all . In each step, moves from a configuration by updating to using the transition rule of and then sampling both...
We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.
We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.
We present a new fundamental intuition forwhy the Kemeny feature of a Markov chain is a constant. This new perspective has interesting further implications.
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