English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider the forward Kolmogorov equation corresponding to measure-valuedprocesses stemming from a class of interacting particle systems in populationdynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Underthe assumption of detailed balance, we provide a rigorous generalized gradientstructure, incorporating the fluxes arising from the birth and death of theparticles.  Moreover, in the large population limit, we show convergence of the forwardKolmogorov equation to a Liouville equation, which is a transport equationassociated with the mean-field limit of the underlying process. In addition, weshow convergence of the corresponding gradient structures in the sense ofEnergy-Dissipation Principles, from which we establish a propagation of chaosresult for the particle system and derive a generalized gradient-flowformulation for the mean-field limit.

Generalized gradient structures for measure-valued population dynamics and their large-population limit