Related papers: Metastability in Stochastic Replicator Dynamics
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
This paper provides an overview of the research on the metastable behavior of the Ising model. We analyze the transition times from the set of metastable states to the set of the stable states by identifying the critical configurations that…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
The dynamical transition occurring in spin-glass models with one step of Replica-Symmetry-Breaking is a mean-field artifact that disappears in finite systems and/or in finite dimensions. The critical fluctuations that smooth the transition…
This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independent patterns $\xi_1,...,\xi_p$ where the patterns have…
We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…
We consider a dynamical system in R driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Levy noise of small intensity and such that the heaviest tail…
Metastability is an ubiquitous phenomenon in nature, which interests several fields of natural sciences. Its description in the framework of thermodynamics and statistical mechanics has been a taboo for long time since it is a genuine…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
We study the behavior of a stochastic variant of replicator dynamics in two-agent zero-sum games. We characterize the statistics of such systems by their invariant measures which can be shown to be entirely supported on the boundary of the…
This work is devoted to quantifying how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit expression for approximating the rate change is provided,…
Logit Dynamics [Blume, Games and Economic Behavior, 1993] are randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
There are multiple ways in which a stochastic system can be out of statistical equilibrium. It might be subject to time-varying forcing; or be in a transient phase on its way towards equilibrium; it might even be in equilibrium without us…
The paper contains the attempt to integration of the classical evolutionary game theory based on replicator dynamics and the state based approach of Houston and Mcnamara. In the new approach, individuals have different heritable strategies,…
We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the…
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small…
We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi…
We introduce a general class of mean-field-like spin systems with random couplings that comprises both the Ising model on inhomogeneous dense random graphs and the randomly diluted Hopfield model. We are interested in quantitative estimates…
Classical metastability manifests as noise-driven switching between disjoint basins of attraction and slowing down of relaxation, quantum systems like qubits and Rydberg atoms exhibit analogous behavior through collective quantum jumps and…