Related papers: Pointwise estimates and exponential laws in metast…
We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…
We explore the dynamics of quantum spin systems in two and three dimensions using an exact mapping to classical stochastic processes. In recent work we explored the effectiveness of sampling around the mean field evolution as determined by…
Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the…
We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential…
The coupling-constant metamorphosis is applied to modified extended Hamiltonians and sufficient conditions are found in order that the transformed high-degree first integral of the transformed Hamiltonian is determined by the same algorithm…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
Motivated by the study of the metastable stochastic Ising model at subcritical temperature and in the limit of a vanishing magnetic field, we extend the notion of ($\kappa$, $\lambda$)-capacities between sets, as well as the associated…
The ability to support metastable current-carrying states in multiply-connected settings is one of the prime signatures of superfluidity. Such states are investigated theoretically for the case of trapped Bose condensed alkali gases,…
This paper studies large deviations of a ``fully coupled" finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment…
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
For nonlinear analytic control systems, we introduce a new paradigm for dynamic output feedback stabilization. We propose to periodically sample the usual observer based control law, and to reshape it so that it coincides with a ''control…
We study the metastable behavior of diffusion processes in narrow tube domains, where the metastability is induced by entropic barriers. We identify a sequence of characteristic time scales $\{T_\epsilon^i\}_{1 \leq i \leq \abs{V'}}$ and…
The Kuramoto model with mixed signs of couplings is known to produce a traveling-wave synchronized state. Here, we consider an abrupt synchronization transition from the incoherent state to the traveling-wave state through a long-lasting…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
We study exit times from a set for a family of multivariate autoregressive processes with normally distributed noise. By using the large deviation principle, and other methods, we show that the asymptotic behavior of the exit time depends…
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when…
We explore the concept of metastability in random dynamical systems, focussing on connections between random Perron-Frobenius operator cocycles and escape rates of random maps, and on topological entropy of random shifts of finite type. The…
We analyze the efficiency of the Wang-Landau algorithm to sample a multimodal distribution on a prototypical simple test case. We show that the exit time from a metastable state is much smaller for the Wang Landau dynamics than for the…
We study the large deviations of the magnetization at some finite time in the Curie-Weiss Random Field Ising Model with parallel updating. While relaxation dynamics in an infinite time horizon gives rise to unique dynamical trajectories…