Random walks on finite groups converging after finite number of steps
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Random walks on finite groups converging after finite number of steps
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| Creator |
Vyshnevetskiy, A.L.
Zhmud, E.M. |
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| Description |
Let P be a probability on a finite group G, P(n)=P∗…∗P (n times) be an n-fold convolution of P. If n→∞, then under mild conditions P(n) converges to the uniform probability U(g)=1|G| (g∈G). We study the case when the sequence P(n) reaches its limit U after finite number of steps: P(k)=P(k+1)=⋯=U for some k. Let Ω(G) be a set of the probabilities satisfying to that condition. Obviously, U∈Ω(G). We prove that Ω(G)≠U for ``almost all'' non-Abelian groups and describe the groups for which Ω(G)=U. If P∈Ω(G), then P(b)=U, where b is the maximal degree of irreducible complex representations of the group G.
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| Date |
2019-06-14T03:38:17Z
2019-06-14T03:38:17Z 2008 |
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| Type |
Article
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| Identifier |
Random walks on finite groups converging after finite number of steps / A.L. Vyshnevetskiy, E.M. Zhmud // Algebra and Discrete Mathematics. — 2008. — Vol. 7, № 2. — С. 123–129. — Бібліогр.: 3 назв. — англ.
1726-3255 2000 Mathematics Subject Classification: 20P05, 60B15. http://dspace.nbuv.gov.ua/handle/123456789/153370 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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