Zobrazeno 1 - 10
of 165
pro vyhledávání: '"70F45"'
Autor:
Schiavo, Lorenzo Dello
We develop a unifying theory for four different objects: (1) infinite systems of interacting massive particles; (2) solutions to the Dean-Kawasaki equation with singular drift and space-time white noise; (3) Wasserstein diffusions with a.s. purely at
Externí odkaz:
http://arxiv.org/abs/2411.14936
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution $f_N(t)$ is gover
Externí odkaz:
http://arxiv.org/abs/2411.08614
For an untilted Frenkel-Kontorova chain and any rational $p/q$, Aubry and Mather proved there are minimising equilibrium states that are left- and right-asymptotic to neighbouring pairs of spatially periodic minimisers of type $(p,q)$. They are known
Externí odkaz:
http://arxiv.org/abs/2408.14124
Autor:
Ingimarson, Benjamin, Pego, Robert L.
We prove the existence of small solitary waves for one-dimensional lattices of particles that each repel every other particle with a force that decays as a power of distance. For force exponents $\alpha+1$ with $\frac43<\alpha<3$, we employ fixed-poi
Externí odkaz:
http://arxiv.org/abs/2406.09184
Autor:
Vaes, U
The aim of this note is to revisit propagation of chaos for a Langevin-type interacting particle system used for sampling probability measures. The interacting particle system we consider coincides, in the setting of a log-quadratic target distributi
Externí odkaz:
http://arxiv.org/abs/2404.06456
Autor:
Davies, Cameron
We study a two parameter family of energy minimization problems for interaction energies $\mathcal{E}_{\alpha,\beta}$ with attractive-repulsive potential $W_{\alpha,\beta}$. We develop a concavity principle, which allows us to provide a lower bound o
Externí odkaz:
http://arxiv.org/abs/2404.02322
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including problems such
Externí odkaz:
http://arxiv.org/abs/2402.01593
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to the finite e
Externí odkaz:
http://arxiv.org/abs/2312.07373
Autor:
Averboukh, Yurii
We study a nonlocal balance equation that describes the evolution of a system consisting of infinitely many identical particles those move along a deterministic dynamics and can also either disappear or give a spring. In this case, the solution of th
Externí odkaz:
http://arxiv.org/abs/2311.01215
We propose an infinite Kuramoto model for a countably infinite set of Kuramoto oscillators and study its emergent dynamics for two classes of network topologies. For a class of symmetric and row(or column)-summable network topology, we show that a ho
Externí odkaz:
http://arxiv.org/abs/2309.16538