Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction
This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of ty...
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| Veröffentlicht in: | Chinese annals of mathematics. Serie B 2022-03, Vol.43 (2), p.195-208 |
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| container_title | Chinese annals of mathematics. Serie B |
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| creator | Zhao, Tong |
| description | This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type
A
or
a
. Under suitable scaling, the local proportion functions of
A
particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method. |
| doi_str_mv | 10.1007/s11401-022-0311-z |
| format | Article |
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A
or
a
. Under suitable scaling, the local proportion functions of
A
particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method.</description><identifier>ISSN: 0252-9599</identifier><identifier>EISSN: 1860-6261</identifier><identifier>DOI: 10.1007/s11401-022-0311-z</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Continuity (mathematics) ; Convergence ; Mathematics ; Mathematics and Statistics ; Partial differential equations ; Tightness ; White noise</subject><ispartof>Chinese annals of mathematics. Serie B, 2022-03, Vol.43 (2), p.195-208</ispartof><rights>The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2022</rights><rights>The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2022.</rights><rights>Copyright © Wanfang Data Co. Ltd. All Rights Reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c230t-bdeed87161c14f3f363d2421af924f17357617b40f6ee0d48fd79c1b521258953</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://www.wanfangdata.com.cn/images/PeriodicalImages/sxnk-e/sxnk-e.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11401-022-0311-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11401-022-0311-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Zhao, Tong</creatorcontrib><title>Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction</title><title>Chinese annals of mathematics. Serie B</title><addtitle>Chin. Ann. Math. Ser. B</addtitle><description>This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type
A
or
a
. Under suitable scaling, the local proportion functions of
A
particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method.</description><subject>Applications of Mathematics</subject><subject>Continuity (mathematics)</subject><subject>Convergence</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial differential equations</subject><subject>Tightness</subject><subject>White noise</subject><issn>0252-9599</issn><issn>1860-6261</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEURYMoWKs_wN2AC1fR9zKTzMxSih-Fgop1HdKZpKZ2MjWZUttfb8qIXbl6cDn38jiEXCLcIEB-GxAzQAqMUUgR6e6IDLAQQAUTeEwGwDijJS_LU3IWwgIAs5zDgLxObGO7kLQmeXaa1rbRLtjWqWUydp32quqsmycvyne2WurkbRs63YRkY7uPZLppaahUjP_Y1p2TE6OWQV_83iF5f7ifjp7o5PlxPLqb0Iql0NFZrXVd5CiwwsykJhVpzTKGypQsM5inPBeYzzIwQmuos8LUeVnhjDNkvCh5OiTX_e5GOaPcXC7atY9_Bxm-3afULLoABpBG8qonV779WuvQHVAmuChYiVBGCnuq8m0IXhu58rZRfisR5N6x7B3LuCv3juUudljfCZF1c-0Py_-XfgCJs34l</recordid><startdate>20220301</startdate><enddate>20220301</enddate><creator>Zhao, Tong</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>School of Mathematical Sciences,Fudan University,Shanghai 200433,China</general><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20220301</creationdate><title>Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction</title><author>Zhao, Tong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c230t-bdeed87161c14f3f363d2421af924f17357617b40f6ee0d48fd79c1b521258953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Continuity (mathematics)</topic><topic>Convergence</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial differential equations</topic><topic>Tightness</topic><topic>White noise</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhao, Tong</creatorcontrib><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Chinese annals of mathematics. Serie B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhao, Tong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction</atitle><jtitle>Chinese annals of mathematics. Serie B</jtitle><stitle>Chin. Ann. Math. Ser. B</stitle><date>2022-03-01</date><risdate>2022</risdate><volume>43</volume><issue>2</issue><spage>195</spage><epage>208</epage><pages>195-208</pages><issn>0252-9599</issn><eissn>1860-6261</eissn><abstract>This paper characterizes the limits of a large system of interacting particles distributed on the real line. The interaction occurring among neighbors involves two kinds of independent actions with different rates. This system is a generalization of the voter process, of which each particle is of type
A
or
a
. Under suitable scaling, the local proportion functions of
A
particles converge to continuous functions which solve a class of stochastic partial differential equations driven by Fisher-Wright white noise. To obtain the convergence, the tightness of these functions is derived from the moment estimate method.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s11401-022-0311-z</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0252-9599 |
| ispartof | Chinese annals of mathematics. Serie B, 2022-03, Vol.43 (2), p.195-208 |
| issn | 0252-9599 1860-6261 |
| language | eng |
| recordid | cdi_wanfang_journals_sxnk_e202202003 |
| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Continuity (mathematics) Convergence Mathematics Mathematics and Statistics Partial differential equations Tightness White noise |
| title | Limits of One-dimensional Interacting Particle Systems with Two-scale Interaction |
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