Exclusion statistics and lattice random walks
We establish a connection between exclusion statistics with arbitrary integer exclusion parameter g and a class of random walks on planar lattices, relating the generating function for the algebraic area of closed walks on the lattice to the grand partition function of particles obeying exclusion st...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2019-11-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321319302172 |
| _version_ | 1818846847649710080 |
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| author | Stéphane Ouvry Alexios P. Polychronakos |
| author_facet | Stéphane Ouvry Alexios P. Polychronakos |
| author_sort | Stéphane Ouvry |
| collection | DOAJ |
| description | We establish a connection between exclusion statistics with arbitrary integer exclusion parameter g and a class of random walks on planar lattices, relating the generating function for the algebraic area of closed walks on the lattice to the grand partition function of particles obeying exclusion statistics g. Square lattice random walks, described in terms of the Hofstadter Hamiltonian, correspond to g=2. In the g=3 case we construct a corresponding chiral random walk on a triangular lattice, and we point to potential random walk models for higher g. In this context, we also derive the form of the microscopic cluster coefficients for arbitrary exclusion statistics and one-body spectrum. |
| first_indexed | 2024-12-19T05:52:04Z |
| format | Article |
| id | doaj.art-03ec785193074ae5b8564e4430c26908 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-19T05:52:04Z |
| publishDate | 2019-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-03ec785193074ae5b8564e4430c269082022-12-21T20:33:35ZengElsevierNuclear Physics B0550-32132019-11-01948Exclusion statistics and lattice random walksStéphane Ouvry0Alexios P. Polychronakos1LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay Cedex, FranceDepartment of Physics, City College of New York, NY 10038, USA; Corresponding author.We establish a connection between exclusion statistics with arbitrary integer exclusion parameter g and a class of random walks on planar lattices, relating the generating function for the algebraic area of closed walks on the lattice to the grand partition function of particles obeying exclusion statistics g. Square lattice random walks, described in terms of the Hofstadter Hamiltonian, correspond to g=2. In the g=3 case we construct a corresponding chiral random walk on a triangular lattice, and we point to potential random walk models for higher g. In this context, we also derive the form of the microscopic cluster coefficients for arbitrary exclusion statistics and one-body spectrum.http://www.sciencedirect.com/science/article/pii/S0550321319302172 |
| spellingShingle | Stéphane Ouvry Alexios P. Polychronakos Exclusion statistics and lattice random walks Nuclear Physics B |
| title | Exclusion statistics and lattice random walks |
| title_full | Exclusion statistics and lattice random walks |
| title_fullStr | Exclusion statistics and lattice random walks |
| title_full_unstemmed | Exclusion statistics and lattice random walks |
| title_short | Exclusion statistics and lattice random walks |
| title_sort | exclusion statistics and lattice random walks |
| url | http://www.sciencedirect.com/science/article/pii/S0550321319302172 |
| work_keys_str_mv | AT stephaneouvry exclusionstatisticsandlatticerandomwalks AT alexiosppolychronakos exclusionstatisticsandlatticerandomwalks |