Random walks on periodic graphs

DOI10.1090/S0002-9947-08-04451-6zbMath1149.60026OpenAlexW2132949527WikidataQ60961390 ScholiaQ60961390MaRDI QIDQ3532557

Kôhei Uchiyama, Takahiro Kazami

Publication date: 28 October 2008

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-08-04451-6

zbMATH Keywords

asymptotic expansionGreen functionMarkov additive processperiodic graphhitting distribution of a line

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Probabilistic potential theory (60J45)

Related Items (6)

Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs ⋮ Local limit theorem for a Markov additive process on with a null recurrent internal Markov chain ⋮ Cyclic products and optimal traps in cyclic birth and death chains ⋮ A local limit theorem for a transient chaotic walk in a frozen environment ⋮ Long time asymptotics of non-symmetric random walks on crystal lattices ⋮ The hitting distributions of a line for two dimensional random walks

Cites Work

• Asymptotic behavior of the transition probability of a random walk on an infinite graph
• Théorie du renouvellement pour des chaînes semi-markoviennes transientes. (Renewal theory for transient semi-Markov chains)
• Local limit theorem for random walk in periodic environment.
• Albanese maps and off diagonal long time asymptotics for the heat kernel
• Asymptotic estimates of the Green functions and transition probabilities for Markov additive processes
• Green's Functions for Random Walks on Z^N
• Markov additive processes. II
• Random walks with internal degrees of freedom
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