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| Seminari A.A. 2019-2020 |
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Relatore |
Titolo |
Data |
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Christoph Lehner
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17 dicembre 2019 |
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Chiara Boccato
IST Austria |
12 novembre 2019 |
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Maxime Hauray
Univeristé Aix-Marseille |
05 novembre 2019 |
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Nguyen Tong Xuan
GSSI L'Aquila |
28 ottobre 2019 (lunedì) |
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Abstract ritorna |
We study the convergence of cluster and virial expansions for systems
of particles subject to positive two-body interactions. Our results
strengthen and generalize existing lower bounds on the radii of
convergence and on the value of the pressure. Our treatment of the
cluster coefficients is based on expressing the truncated weights in
terms of trees and partition schemes, and generalize to soft
repulsions previous approaches for models with hard exclusions. Our
main theorem holds in a very general framework that does not require
translation invariance and is applicable to models in general measure
spaces. For the virial coefficients we resort to an approach due to
Ramawadth and Tate that avoids Lagrange inversion techniques and leads
to diagrammatic expressions in terms of trees, rather than the doubly
connected diagrams traditionally used. We obtain a new criterion that
strengthens, for repulsive interactions, the best criterion previously
available (proposed by Groenveld and proven by Ramawadth and Tate). We
illustrate our results with a few applications showing noticeable
improvements in the lower bound of convergence radii.
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Sara Daneri
GSSI L'Aquila |
22 ottobre 2019 |
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Horst Knörrer
ETH Zürich |
15 ottobre 2019 |
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