Vacancy localisation in the square dimer model, statistics of geodesic in large quadrangulations
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| Description: |
Bouttier, J (CEA Saclay)
Monday 21 April 2008, 15:30-16:30 Statistical-Mechanics and Quantum-Field Theory Methods in Combinatorial Enumeration |
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| Created: | 2008-04-30 13:42 | ||
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| Collection: | Combinatorics and Statistical Mechanics | ||
| Publisher: | Isaac Newton Institute | ||
| Copyright: | Bouttier, J | ||
| Language: | eng (English) | ||
| Distribution: |
World
(downloadable)
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| Credits: |
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| Explicit content: | No | ||
| Aspect Ratio: | 4:3 | ||
| Screencast: | No | ||
| Bumper: | /sms-ingest/static/new-4x3-bumper.dv | ||
| Trailer: | /sms-ingest/static/new-4x3-trailer.dv | ||
| Abstract: | I shall present two independent projects carried out last year, illustrating the interests of a typical combinatorial statistical mechanist.
- I first consider the classical dimer model on a square lattice with a single vacancy, and address the question of the possible motion of the vacancy induced by dimer slidings. Adapting a variety of techniques (Temperley bijection, matrix tree theorem, finite-size analysis, numerical simulations), we find that the vacancy remains localized albeit in a very weak fashion, leading to non-trivial diffusion exponents. [joint work with M. Bowick, E. Guitter and M. Jeng] - I next consider the statistical properties of geodesics in large random planar quadrangulations. Introducing "spine trees" extending Schaeffer's well-labeled tree construction, we obtain in particular the generating function for quadrangulations with a marked geodesic. We deduce exact statistics for large quadrangulations both in the "local" and "scaling" limits. [joint work with E. Guitter] |
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