Related papers: Mean-Field Limits for Nearly Unstable Hawkes Proce…
It is commonly believed that a massive real scalar field $\phi$ only mediates short-range interactions on the scale of its Compton wavelength via the Yukawa potential. However, in the nonperturbative regime of nonlinear self coupling,…
We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit…
We prove propagation of chaos in the Random field mean-field Ising model, also known ad the Random field Curie-Weiss model. We show that in the paramagnetic phase, i.e.\ in the regime where temperature and distribution of the external field…
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…
The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $\alpha$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional…
We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation…
This paper studies a class of mixed mean-field jump processes on an abstract state space $\Pi$, together with their associated $N$-particle systems. The dynamics consist of the superposition of an independent Markovian component and a…
We provide a generic way of deducing non-asymptotic error bounds for Sequential MCMC methods from suitable stability properties of Feynman-Kac propagators. We show how to derive this type of stability from mixing conditions for the MCMC…
Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such approach promises to reach the fundamental Heisenberg scaling as a…
We introduce an anisotropic mean-field approach for the dynamics of semiflexible polymers under intermediate tension, the force range where a chain is partially extended but not in the asymptotic regime of a nearly straight contour. The…
This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of…
We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes…
We study large time behavior of critical marked Hawkes processes and related branching particle systems. In case of marked Hawkes processes we assume that the kernel function has multiplicative form and the marks corresponding to the events…
The $\lambda \phi^4$ model in a finite volume is studied within a non-gaussian Hartree-Fock approximation (tdHF) both at equilibrium and out of equilibrium, with particular attention to the structure of the ground state and of certain…
In this work, we formulate an abstract framework to study mean-field systems. In contrast to most approaches in the available literature which primarily rely on the analysis of SDEs, ours is based on optimal transport and semigroup theory.…
The Sierpinski gasket is known to support an exotic stochastic process called the asymptotically one-dimensional diffusion. This process displays local anisotropy, as there is a preferred direction of motion which dominates at the…
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 consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…
We provide an error bound for approximating the time evolution of N bosons by a generalized nonlinear Hartree equation. The bosons are assumed to interact via permutation symmetric bounded many-particle potentials and the initial…
The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a…