Long time behavior of random walks on abelian groups

• Autorzy: Alexander Bendikov , Barbara Bobikau
• Języki publikacji: EN

Abstrakty

EN

Let 𝔾 be a locally compact non-compact metric group. Assuming that 𝔾 is abelian we construct symmetric aperiodic random walks on 𝔾 with probabilities $n ↦ ℙ(S_{2n} ∈ V)$ of return to any neighborhood V of the neutral element decaying at infinity almost as fast as the exponential function n ↦ exp(-n). We also show that for some discrete groups 𝔾, the decay of the function $n ↦ ℙ(S_{2n} ∈ V)$ can be made as slow as possible by choosing appropriate aperiodic random walks Sₙ on 𝔾.

Kategorie tematyczne

• 62E10: Characterization and structure theory
• 43A05: Measures on groups and semigroups, etc.
• 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
• 60-02: Research exposition (monographs, survey articles)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 118
• Numer: 2
• Strony: 445-464

Daty

wydano

2010

Twórcy

autor

Alexander Bendikov

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Barbara Bobikau

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Identyfikatory

DOI

10.4064/cm118-2-6