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Tesi di dottorato in scienze matematiche e fisiche >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/2108/483
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| DC Field | Value | Language |
|---|
| contributor.advisor | Cerf, Raphael | - |
| contributor.advisor | Olivieri, Enzo | - |
| contributor.author | Gaudillière, Alexandre | - |
| date.accessioned | 2008-05-13T13:09:55Z | - |
| date.available | 2008-05-13T13:09:55Z | - |
| date.issued | 2008-05-13T13:09:55Z | - |
| identifier.uri | http://hdl.handle.net/2108/483 | - |
| description | 19. ciclo | en |
| description.abstract | We study the escape from metastability for a gas of particles under the conservative
Kawasaki dynamics at low temperature and inside a two-dimensional box
with exponentially large volume in the inverse temperature.
We first analyse the typical trajectories followed by the system, in the local
version of the model, during the first transition between metastability and stability.
We describe geometrically the configurations along these typical trajectories and
we show that the whole evolution goes, with very large probability, from “quasisquares”
to larger “quasi-squares” and that the growing cluster of this nucleation
process “wanders” around the box which it is contained in. In addition, along these
trajectories, the fluctuations of the dimensions of the cluster are bounded: if a
rectangle l×L circumscribes one of these clusters then L−l 1+2pL. We show that
fluctuations of this order cannot be neglected: they take place with probabilities
that are “non exponentially small” in . As a consequence the process is very
different from the typical nucleation of the non-conservative Glauber dynamics,
especially as far as the supercritical part is concerned.
Then we prove a property of planar random walks which allows to extend the
results obtained for the local version of the model to the original Kawasaki dynamics.
We give a lower bound of the non-collision probability in a long tine T for a system
of n random walks with fixed obstacles. By “collision” we mean collision with
the fixed obstacles as well between the particles themselves. We explain how this
property allows to describe in terms of “Quasi Random Walks” a rarefied gas of
particles under the Kawasaki dynamics.
On the basis of these results we can predict the main features of the escape from
metastability for the original Kawasaki dynamics. | en |
| format.extent | 11854499 bytes | - |
| format.mimetype | application/pdf | - |
| language.iso | fr | en |
| subject | metastability | en |
| subject | conservative dynamics | en |
| subject | Kawasaki dynamics | en |
| subject | nucleation | en |
| subject | non-collision probability | en |
| subject | potential theory | en |
| title | Fuite de la métastabilité pour dynamiques stochastiques conservatives | en |
| title.alternative | Fuga dalla metastabilità per dinamiche stocastiche conservative | en |
| type | Doctoral thesis | en |
| degree.level | Dottorato | en |
| degree.discipline | Facoltà di Scienze Matematiche Fisiche e Naturali | en |
| degree.grantor | Università degli studi di Roma Tor Vergata | en |
| date.dateofdefense | A.A. 2005/2006 | en |
| Appears in Collections: | Tesi di dottorato in scienze matematiche e fisiche
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Files in This Item:
| File |
Description |
Size | Format |
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| tesi.pdf | | 11576Kb | Adobe PDF | View/Open |
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