Random walks on finite groups converging after finite number of steps
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...
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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2008
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153370 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1533702019-06-15T01:25:43Z Random walks on finite groups converging after finite number of steps Vyshnevetskiy, A.L. Zhmud, E.M. 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. 2008 Article 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 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Vyshnevetskiy, A.L. Zhmud, E.M. |
| spellingShingle |
Vyshnevetskiy, A.L. Zhmud, E.M. Random walks on finite groups converging after finite number of steps Algebra and Discrete Mathematics |
| author_facet |
Vyshnevetskiy, A.L. Zhmud, E.M. |
| author_sort |
Vyshnevetskiy, A.L. |
| title |
Random walks on finite groups converging after finite number of steps |
| title_short |
Random walks on finite groups converging after finite number of steps |
| title_full |
Random walks on finite groups converging after finite number of steps |
| title_fullStr |
Random walks on finite groups converging after finite number of steps |
| title_full_unstemmed |
Random walks on finite groups converging after finite number of steps |
| title_sort |
random walks on finite groups converging after finite number of steps |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153370 |
| citation_txt |
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. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:38:47Z |
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