Fourier Analysis on Groups, Random Walks and Markov Chains

2019 ◽  
pp. 231-270
Author(s):  
Kenneth W. Johnson
Keyword(s):  
Markov Chains ◽  
Fourier Analysis ◽  
Random Walks

scholarly journals Quantum Markov Chains Associated with Open Quantum Random Walks

2019 ◽  
Vol 176 (5) ◽  
pp. 1272-1295 ◽  
Author(s):  
Ameur Dhahri ◽  
Chul Ki Ko ◽  
Hyun Jae Yoo
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Quantum Random Walks ◽  
Open Quantum ◽  
Open Quantum Random Walks ◽  
Quantum Markov Chains

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.

Random walks on discrete and continuous circles

1993 ◽  
Vol 30 (4) ◽  
pp. 780-789 ◽  
Author(s):  
Jeffrey S. Rosenthal
Keyword(s):  
Random Walk ◽  
Fourier Analysis ◽  
Random Walks ◽  
Large Class ◽  
Lipschitz Function ◽  
Generation Gap

We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the ‘generation gap' process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the continuous circle S1.

scholarly journals Gaussian Estimates for Markov Chains and Random Walks on Groups

1993 ◽  
Vol 21 (2) ◽  
pp. 673-709 ◽  
Author(s):  
W. Hebisch ◽  
L. Saloff-Coste
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Random Walks On Groups ◽  
Gaussian Estimates

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.

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