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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2008 |
| ISSN: | 1726-3255 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/153370 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862549622474407936 |
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| author | Vyshnevetskiy, A.L. Zhmud, E.M. |
| author_facet | Vyshnevetskiy, A.L. Zhmud, E.M. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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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| first_indexed | 2025-11-25T20:37:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-153370 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T20:37:07Z |
| publishDate | 2008 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Vyshnevetskiy, A.L. Zhmud, E.M. 2019-06-14T03:38:17Z 2019-06-14T03:38:17Z 2008 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. https://nasplib.isofts.kiev.ua/handle/123456789/153370 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Random walks on finite groups converging after finite number of steps Article published earlier |
| spellingShingle | Random walks on finite groups converging after finite number of steps Vyshnevetskiy, A.L. Zhmud, E.M. |
| title | 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_short | Random walks on finite groups converging after finite number of steps |
| title_sort | random walks on finite groups converging after finite number of steps |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/153370 |
| work_keys_str_mv | AT vyshnevetskiyal randomwalksonfinitegroupsconvergingafterfinitenumberofsteps AT zhmudem randomwalksonfinitegroupsconvergingafterfinitenumberofsteps |