Benvenuti nell'Anagrafe della Ricerca d'Ateneo
La valutazione delle attività di ricerca che si svolgono nelle università ha assunto un'importanza rilevante sia per l'intero sistema universitario sia all'interno di ogni singolo ateneo. Roma Tre si è quindi dotata di idonei strumenti informativi in grado di supportare al meglio le azioni di monitoraggio e di valutazione delle attività di ricerca svolte nei propri dipartimentied ha realizzato una Anagrafe della Ricerca di Ateneo.
EnglishOn the rooted k-ary tree we consider a 0-1 kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are empty. For this process the following picture was conjectured to hold. As long as p is below the percolation threshold pc = 1/k the process is ergodic with a finite relaxation time while, for p > pc, the process on the infinite tree is no longer ergodic and the relaxation time on a finite regular sub-tree becomes exponentially large in the depth of the tree. At the critical point p = pc the process on the infinite tree is still ergodic but with an infinite relaxation time. Moreover, on finite sub-trees, the relaxation time grows polynomially in the depth of the tree. The conjecture was recently proved by the second and forth author except at crit- icality. Here we analyse the critical and quasi-critical case and prove for the relevant time scales: (i) power law behaviour in the depth of the tree at p = pc and (ii) power law scaling in (pc − p)−1 when p approaches pc from below. Our results, which are very close to those obtained recently for the Ising model at the spin glass critical point, represent the first rigorous analysis of a kinetically constrained model at criticality.
CANCRINI NICOLETTA, MARTINELLI FABIO, ROBERTO CYRIL, & TONINELLI CRISTINA (2015). Mixing time of a kinetically constrained spin model on trees: power law scaling at criticality. PROBABILITY THEORY AND RELATED FIELDS, 161(1-2), 247-266.
| Titolo: | Mixing time of a kinetically constrained spin model on trees: power law scaling at criticality |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Citazione: | CANCRINI NICOLETTA, MARTINELLI FABIO, ROBERTO CYRIL, & TONINELLI CRISTINA (2015). Mixing time of a kinetically constrained spin model on trees: power law scaling at criticality. PROBABILITY THEORY AND RELATED FIELDS, 161(1-2), 247-266. |
| Handle: | http://hdl.handle.net/11590/136792 |
| ISBN: | 0178-8051 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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