Publicação
Simple exclusion process : from randomness to determinism
| Resumo: | In this work I introduce a classical example of an Interacting Particle System: the Simple Exclusion Process. I present the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and an heuristic argument to derive from the microscopic dynamics between particles a partial differential equation describing the evolution of the density profile. For the Simple Exclusion Process, in the Symmetric case ($p=1/2$) we will get to the heat equation while in the Asymmetric case ($p\neq{1/2}$) to the inviscid Burgers equation. Finally, I introduce the Central Limit Theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic partial differential equation. |
|---|---|
| Autores principais: | Gonçalves, Patrícia |
| Assunto: | Particle systems Exclusion dynamics |
| Ano: | 2011 |
| País: | Portugal |
| Tipo de documento: | comunicação em conferência |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| _version_ | 1867437956779737088 |
|---|---|
| author | Gonçalves, Patrícia |
| author_facet | Gonçalves, Patrícia |
| author_role | author |
| contributor_name_str_mv | RepositóriUM - Universidade do Minho |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Gonçalves, Patrícia\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | RepositóriUM - Universidade do Minho |
| datacite.creators.creator.creatorName.fl_str_mv | Gonçalves, Patrícia |
| datacite.date.Accepted.fl_str_mv | 2011-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2012-02-08T12:19:26Z |
| datacite.date.embargoed.fl_str_mv | 2012-02-08T12:19:26Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Particle systems Exclusion dynamics |
| datacite.titles.title.fl_str_mv | Simple exclusion process : from randomness to determinism |
| dc.contributor.none.fl_str_mv | RepositóriUM - Universidade do Minho |
| dc.creator.none.fl_str_mv | Gonçalves, Patrícia |
| dc.date.Accepted.fl_str_mv | 2011-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2012-02-08T12:19:26Z |
| dc.date.embargoed.fl_str_mv | 2012-02-08T12:19:26Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | https://hdl.handle.net/1822/16915 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | Springer |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Particle systems Exclusion dynamics |
| dc.title.fl_str_mv | Simple exclusion process : from randomness to determinism |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_5794 |
| description | In this work I introduce a classical example of an Interacting Particle System: the Simple Exclusion Process. I present the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and an heuristic argument to derive from the microscopic dynamics between particles a partial differential equation describing the evolution of the density profile. For the Simple Exclusion Process, in the Symmetric case ($p=1/2$) we will get to the heat equation while in the Asymmetric case ($p\neq{1/2}$) to the inviscid Burgers equation. Finally, I introduce the Central Limit Theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic partial differential equation. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | conferencePaper |
| fulltext.url.fl_str_mv | https://repositorium.uminho.pt/bitstreams/93e2d0a2-80c2-48a5-83ec-9de10c74bf18/download |
| id | rum_0bb6e67aa43feb23ea85bd49ff82c3cb |
| identifier.url.fl_str_mv | https://hdl.handle.net/1822/16915 |
| instacron_str | repositorium |
| institution | Universidade do Minho |
| instname_str | Universidade do Minho |
| language | eng |
| network_acronym_str | rum |
| network_name_str | RepositóriUM - Universidade do Minho |
| oai_identifier_str | oai:repositorium.uminho.pt:1822/16915 |
| organization_str_mv | urn:organizationAcronym:repositorium |
| person_str_mv | Gonçalves, Patrícia |
| publishDate | 2011 |
| publisher.none.fl_str_mv | Springer |
| reponame_str | RepositóriUM - Universidade do Minho |
| repository_id_str | urn:repositoryAcronym:rum |
| service_str_mv | urn:repositoryAcronym:rum |
| spelling | engSpringerporIn this work I introduce a classical example of an Interacting Particle System: the Simple Exclusion Process. I present the notion of hydrodynamic limit, which is a Law of Large Numbers for the empirical measure and an heuristic argument to derive from the microscopic dynamics between particles a partial differential equation describing the evolution of the density profile. For the Simple Exclusion Process, in the Symmetric case ($p=1/2$) we will get to the heat equation while in the Asymmetric case ($p\neq{1/2}$) to the inviscid Burgers equation. Finally, I introduce the Central Limit Theorem for the empirical measure and the limiting process turns out to be a solution of a stochastic partial differential equation.application/pdfporSimple exclusion process : from randomness to determinismGonçalves, PatríciaHostingInstitutionOrganizationalRepositóriUM - Universidade do Minhoe-mailmailto:repositorium@usdb.uminho.ptrepositorium@usdb.uminho.ptISBNIsPartOf9783642114557ISSNIsPartOf2190-5614DOIIsPartOf10.1007/978-3-642-11456-4_272012-02-08T12:19:26Z20112011-01-01T00:00:00ZHandlehttps://hdl.handle.net/1822/16915http://purl.org/coar/access_right/c_abf2open accessParticle systemsExclusion dynamics204598 bytesother research producthttp://purl.org/coar/resource_type/c_5794conference paperhttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://repositorium.uminho.pt/bitstreams/93e2d0a2-80c2-48a5-83ec-9de10c74bf18/download |
| spellingShingle | Simple exclusion process : from randomness to determinism Gonçalves, Patrícia Particle systems Exclusion dynamics |
| status | SINGLETON |
| subject.fl_str_mv | Particle systems Exclusion dynamics |
| title | Simple exclusion process : from randomness to determinism |
| title_full | Simple exclusion process : from randomness to determinism |
| title_fullStr | Simple exclusion process : from randomness to determinism |
| title_full_unstemmed | Simple exclusion process : from randomness to determinism |
| title_short | Simple exclusion process : from randomness to determinism |
| title_sort | Simple exclusion process : from randomness to determinism |
| topic | Particle systems Exclusion dynamics |
| topic_facet | Particle systems Exclusion dynamics |
| url | https://hdl.handle.net/1822/16915 |
| visible | 1 |