Towards a rook-theoretic model for ASEP
This thesis analyses the relation between rook covers over Ferrers boards and the Asymetric Exclusion Process (ASEP). A polynomial defined over the set of all possible rook covers has been suggested to be identical to the polynomial that gives the probabilities of the stationary distribution of the...
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| Format: | Others |
| Language: | English |
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KTH, Matematik (Avd.)
2015
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| Online Access: | http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-168568 |
| Summary: | This thesis analyses the relation between rook covers over Ferrers boards and the Asymetric Exclusion Process (ASEP). A polynomial defined over the set of all possible rook covers has been suggested to be identical to the polynomial that gives the probabilities of the stationary distribution of the ASEP. In this thesis a draft is presented of a possible proof by induction of this claim, and parts of this induction are proved. Further results regarding that would follow from the main claim are also independently proved and a complete proof of the claim, invented by another author, is presented for the sake of completeness. === I den här uppsatsen undersöks förhållandet mellan tornplaceringar på Ferrersbräden och den asymmetriska exklusionsprocessen (ASEP). Ett polynom över alla möjliga tornplaceringar har föreslagits vara ekvivalent med polynomet som ger sannolikheterna i den stationära fördelningen för ASEP. Ett utkast till ett induktionsbevis av detta påstående presenteras i den här upsatsen. Vidare resultat kring (q) som skulle följa från detta huvudpåstående bevisas separat och ett mer utförligt bevis av huvudpåståendet skapat av en annan författare presenteras också. |
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