scholarly journals Total Variation Discrepancy of Deterministic Random Walks for Ergodic Markov Chains

2015 ◽  
Author(s):  
Takeharu Shiraga ◽  
Yukiko Yamauchi ◽  
Shuji Kijima ◽  
Masafumi Yamashita
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Total Variation

scholarly journals Total variation discrepancy of deterministic random walks for ergodic Markov chains

2017 ◽  
Vol 699 ◽  
pp. 63-74 ◽  
Author(s):  
Takeharu Shiraga ◽  
Yukiko Yamauchi ◽  
Shuji Kijima ◽  
Masafumi Yamashita
Keyword(s):  
Markov Chains ◽  
Random Walks ◽  
Total Variation

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.

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