Related papers: Polynomial-time sampling despite disorder chaos

We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that…

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…

A two-dimensional system of non-locally coupled complex Ginzburg-Landau oscillators is investigated numerically for the first time. As already known for the one-dimensional case, the system exhibits anomalous spatio-temporal chaos…

Conventional spectral probes of quantum chaos require eigenvalues, and sometimes, eigenvectors of the quantum Hamiltonian. This involves computationally expensive diagonalization procedures. We test whether an unsupervised neural network…

In this note we prove that suitable positive powers of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix converge in law, as the size of the matrix tends to infinity, to a Gaussian…

There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial "refinement" algorithms seem to be very efficient in practice. Some philosophical justification is provided by a classical theorem of…

The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…

We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…

Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…

We study the transport dynamics of matter-waves in the presence of disorder and nonlinearity. An atomic Bose-Einstein condensate that is localized in a quasiperiodic lattice in the absence of atom-atom interaction shows instead a slow…

Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method.…

We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant ensembles, converge in law to Gaussian…

We investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, we show that…

We give the first fully polynomial-time algorithm for learning halfspaces with respect to the uniform distribution on the hypercube in the presence of contamination, where an adversary may corrupt some fraction of examples and labels…

We study the characteristics of chaos evolution of initially localized energy excitations in the one-dimensional nonlinear disordered Klein-Gordon lattice of anharmonic oscillators, by computing the time variation of the fundamental…

In bistable dynamical systems driven by Wiener processes, the widely used Kramers' law relates the strength of the noise forcing to the average time it takes to see a noise-induced transition from one attractor to the other. We extend this…

We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires…

The half-filled attractive Hubbard model exhibits simultaneous charge density wave and superconducting order in its ground state. In this paper we explore the effect of disorder in the site energies on this degeneracy. We find that…