Related papers: Broken ergodicity and memory in the minority game
We discuss in detail the derivation of stochastic differential equations for the continuum time limit of the Minority Game. We show that all properties of the Minority Game can be understood by a careful theoretical analysis of such…
Under an oscillating mechanical drive, an amorphous material progressively forgets its initial configuration and might eventually converge to a limit cycle. Beyond quasistatic drivings, how structurally disordered systems lose or record…
Quantum systems that violate the eigenstate thermalisation hypothesis thereby falling outside the paradigm of conventional statistical mechanics are of both intellectual and practical interest. We show that such a breaking of ergodicity may…
The Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they…
We report the occurrence of quenching and annealing in a version of the Minority Game (MG) in which the winning option is to join a given fraction of the population that is a free, external parameter. We compare this to the different…
Random walk models, such as the trap model, continuous time random walks, and comb models exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is: what statistical mechanical theory replaces the…
We investigate the low temperature behavior of a system in a spontaneously broken symmetry phase described by an Euclidean quantum $\lambda\varphi^{4}_{d+1}$ model with quenched disorder. Using a series representation for the averaged…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
A basic question for zero-sum repeated games consists in determining whether the mean payoff per time unit is independent of the initial state. In the special case of "zero-player" games, i.e., of Markov chains equipped with additive…
Colonel Blotto games with discrete strategy spaces effectively illustrate the intricate nature of multidimensional strategic reasoning. This paper studies the equilibrium set of such games where, in line with prior experimental work, the…
We analyze the minority game for patients, and the results known from the minority game are applied to the patient problem consulted at the department of pediatric cardiology. We find numerically the standard deviation and the global…
We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For a broad class of nonlinearities, we study statistically steady states of the system and find that…
We study the transitions between ergodic and many-body localized phases in spin systems, subject to quenched disorder, including the Heisenberg chain and the central spin model. In both cases systems with common spin lengths $1/2$ and $1$…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
We study a fundamental instability mechanism in nonlinear, nonlocal dynamical systems arising from the interaction of long-range memory and stochastic regime switching. The dynamics are governed by network-coupled, operator-valued Volterra…
Mean field games model equilibria in games with a continuum of players as limiting systems of symmetric $n$-player games with weak interaction between the players. We consider a finite-state, infinite-horizon problem with two cost criteria:…
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation…
The article reports a numerical investigation of the breakdown of a disordered system considering the effect of local stress concentration under the action of an external tensile force. The statistics of the record-breaking magnitudes of…
In the Minority Game (MG), an odd number of heterogeneous and adaptive agents choose between two alternatives and those who end up on the minority side win. When the information available to the agents to make their choice is the identity…
In a mean field game of controls, players seek to minimize a cost that depends on the joint distribution of players' states and controls. We consider an ergodic problem for second-order mean field games of controls with state constraints,…