Markov chains and random walks

2012 ◽  
pp. 191-264
Keyword(s):  
Markov Chains ◽  
Random Walks

scholarly journals Open quantum random walks, quantum Markov chains and recurrence

2019 ◽  
Vol 31 (07) ◽  
pp. 1950020 ◽  
Author(s):  
Ameur Dhahri ◽  
Farrukh Mukhamedov
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Markov Processes ◽  
Transition Operator ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Commutative Subalgebra ◽  
Open Quantum Random Walks ◽  
Quantum Markov Chains

In the present paper, we construct QMCs (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution [Formula: see text] of OQRW. This sheds new light on some properties of the measure [Formula: see text]. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov processes. Furthermore, we study several properties of QMC and associated measures. A new notion of [Formula: see text]-recurrence of QMC is studied, and the relations between the concepts of recurrence introduced in this paper and the existing ones are established.

scholarly journals Chains, entropy, coding

1986 ◽  
Vol 6 (3) ◽  
pp. 415-448 ◽  
Author(s):  
Karl Petersen
Keyword(s):  
Growth Rate ◽  
Markov Chains ◽  
Random Walks ◽  
Finite Type ◽  
Periodic Orbits ◽  
Entropy Coding ◽  
Positive Entropy ◽  
Loop Analysis ◽  
Countable State ◽  
Subshifts Of Finite Type

AbstractVarious definitions of the entropy for countable-state topological Markov chains are considered. Concrete examples show that these quantities do not coincide in general and can behave badly under nice maps. Certain restricted random walks which arise in a problem in magnetic recording provide interesting examples of chains. Factors of some of these chains have entropy equal to the growth rate of the number of periodic orbits, even though they contain no subshifts of finite type with positive entropy; others are almost sofic – they contain subshifts of finite type with entropy arbitrarily close to their own. Attempting to find the entropies of such subshifts of finite type motivates the method of entropy computation by loop analysis, in which it is not necessary to write down any matrices or evaluate any determinants. A method for variable-length encoding into these systems is proposed, and some of the smaller subshifts of finite type inside these systems are displayed.

scholarly journals Hitting Times of Walks on Graphs through Voltages

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
José Luis Palacios ◽  
Eduardo Gómez ◽  
Miguel Del Río
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Hitting Times ◽  
Reciprocity Principle ◽  
Triangular Inequality ◽  
Random Walks On Graphs ◽  
Necklace Graph

We derive formulas for the expected hitting times of general random walks on graphs, in terms of voltages, with very elementary electric means. Under this new light we revise bounds and hitting times for birth-and-death Markov chains and for walks on graphs with cutpoints, and give some exact computations on the necklace graph. We also prove Tetali’s formula for hitting times without making use of the reciprocity principle. In fact this principle follows as a corollary of our argument that also yields as corollaries the triangular inequality for effective resistances and the reversibility of the sum of hitting times around a tour.

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