7 papers
On the Pure States of the Replica Symmetry Breaking ansatz
Simone Franchini
We discuss the concept of Pure State of the Replica Symmetry Breaking ansatz in finite and infinite spin systems without averaging on the disorder, nor using replicas. Consider a s…
Large deviations for Generalized Polya Urns with non-binary increments
Simone Franchini
In this paper we show how to extend the Sample-Path Large Deviation Principle for the urn model of Hill, Lane and Sudderth to the case in which the increment of the urn is not a bi…
The Urn of Hill, Lane and Sudderth
Simone Franchini
We review some facts, properties and applications of the urn of Hill, Lane and Sudderth, a paradigmatic model of stochastic process with memory where the urn evolution is as follow…
On the thermodynamic limit of bipartite spin networks
Simone Franchini
We investigate the properties of the thermodynamic limit in a general bipartite spin network with pairwise interactions. This is done by integrating one of the the spin groups, to…
Blanket representation for spin networks with n-body interactions
Simone Franchini
This paper extends the Blanket representation of [Universal scaling limits for spin networks via martingale methods, Franchini, S., Proc. R. Soc. A, 481 (2025)] from systems with t…
Causal horizon from quantum fluctuations
Simone Franchini
We propose a simple model of quantum void where the flow of time is deduced directly from quantum fluctuations and the consequent particle-antiparticle creations. Given a certain n…