Related papers: Replica Symmetry Breaking in the Random Replicant …
We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non…
We consider a simple decision model in which a set of agents randomly choose one of two competing shops selling the same perishable products (typically food). The satisfaction of agents with respect to a given store is related to the…
In Bayesian inference, computing the posterior distribution from the data is typically a non-trivial problem, which usually requires approximations such as mean-field approaches or numerical methods, like the Monte Carlo Markov Chain. Being…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
We start with a rather detailed, general discussion of recent results of the replica approach to statistical mechanics of a single classical particle placed in a random $N (\gg 1)$-dimensional Gaussian landscape and confined by a…
If Nature is supersymmetric at the weak interaction scale, what can we hope to learn from experiments on supersymmetric particles? The most mysterious aspect of phenomenological supersymmetry is the mechanism of spontaneous supersymmetry…
We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
The planar grasshopper problem, originally introduced in (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494), is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this work…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…
In this thesis, we review and examine the replica method from several viewpoints. The replica method is a mathematical technique to calculate general moments of stochastic variables. This method provides a systematic way to evaluate…
Coexistence of competing species is, due to unavoidable fluctuations, always transient. In this Letter, we investigate the ultimate survival probabilities characterizing different species in cyclic competition. We show that they often obey…
We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character…
Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong, rather than individual qualities. It was recently…
Models of coordinated behavior of populations living in the same environment are introduced for the cases when they either compete with each other, or they both gain by mutual interactions, or finally when one hunts the other one. The…
Dynamical supersymmetry breaking is a fascinating theoretical problem. It is also of phenomenological significance. A better understanding of this phenomenon can help in model building, which in turn is useful in guiding the search for…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…
In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game's payoff entries are random variables. Using the replicator-mutator equations, we…
We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The…