Related papers: Maximal Moments and Uniform Modulus of Continuity …
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral…
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
In this paper, we investigate the robustness of stationary mean-field equilibria in the presence of model uncertainties, specifically focusing on infinite-horizon discounted cost functions. To achieve this, we initially establish…
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…
A sufficient condition for the uniform modulus of continuity of a random field $X = \{X(t), t \in \R^N\}$ is provided. The result is applicable to random fields with heavy-tailed distribution such as stable random fields.
For a class of reducible Hamiltonian partial differential equations (PDEs) with arbitrary spatial dimensions, quantified by a quadratic polynomial with time-dependent coefficients, we present a comprehensive classification of long-term…
We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…
We study the sub-structure of the heterotic Kahler moduli space due to the presence of non-Abelian internal gauge fields from the perspective of the four-dimensional effective theory. Internal gauge fields can be supersymmetric in some…
Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
An important open problem is the theoretically feasible acceleration of mini-batch SGD-type algorithms on quadratic problems with power-law spectrum. In the non-stochastic setting, the optimal exponent $\xi$ in the loss convergence $L_t\sim…
In constrast to discretized space-time approximations to continuum quantum field theories, discretized velocity space approximations to continuum quantum field theories are investigated. A four-momentum operator is given in terms of bare…
We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…
We construct random dynamics on collections of non-intersecting planar contours, leaving invariant the distributions of length- and area-interacting polygonal Markov fields with V-shaped nodes. The first of these dynamics is based on the…
In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For…
The role of memory time fluctuations for instabilities in random media is considered. It is shown that fluctuations can result in infinitely fast growth of statistical moments. The effect is demonstrated in the framework of light…
Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasi-bound states, have been studied both in the linear and nonlinear regimes. In this paper we show that quasi-bound states can form…
We investigate the well-posedness and long-time behavior of a general continuum neural field model with Gaussian noise on possibly unbounded domains. In particular, we give conditions for the existence of invariant probability measures by…