19 citations · 57 across the 9 of their papers we have counts for
9 papers
Elephant Random Walk with multiple extractions
Simone Franchini
Consider a generalized Elephant Random Walk in which the step is chosen by selecting previous steps with odd and then going in the majority direction with a probability …
Large Deviations Theory of Increasing Returns
Simone Franchini, Riccardo Balzan
An influential theory of increasing returns has been proposed by the economist W. B. Arthur in the '80s to explain the lock-in phenomenon between two competing commercial products.…
Energy of the Interacting Self-Avoiding Walk at the point
Simone Franchini, Riccardo Balzan
We perform a numerical study of a new microcanonical polymer model on the three dimensional cubic lattice, consisting of ideal chains whose range and number of nearest-neighbor con…
A simplified Parisi Ansatz
Simone Franchini
Based on simple combinatorial arguments, we formulate a generalized cavity method where the Random Overlap Structure (ROSt) probability space of Aizenmann, Sims and Starr is obtain…
Free energy of bipartite Sherrington-Kirkpatrick model
Liming Pan, Simone Franchini
In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains bo…
Random Polymers and Generalized Urn Processes
Simone Franchini, Riccardo Balzan
We describe a microcanonical approach for polymer models that combines atmospheric methods with urn theory. We show that Large Deviation Properties of urn models can provide quite…
Replica Symmetry Breaking without Replicas
Simone Franchini
We introduce a mathematical framework based on simple combinatorial arguments (Kernel Representation) that allows to deal successfully with spin glass problems, among others. Let $…
Large deviations for Generalized Polya Urns with arbitrary urn function
Simone Franchini
We consider a generalized two-color Polya urn (black and withe balls) first introduced by Hill, Lane, Sudderth where the urn composition evolves as follows: let $π:\left[0,1\right]…
Ideal chains with fixed self-intersection rate
Simone Franchini
We consider ideal chains in a hypercubic lattice \mathbb{Z}^{d}, d\geq3, with a fixed ratio m of self-intersection per monomer. Despite the simplicity of the geometrical constraint…