arXiv subjects

Chun Yin Lam

Publications and source records attributed to Chun Yin Lam.

3 recordsLinked to original sources

arXiv2026

Existence and Non-existence for Continuous Generalized Exchange-Driven Growth model

The continuous generalized exchange-driven growth model (CGEDG) is a coagulation-fragmentation equation that describes the evolution of the macroscopic cluster size distribution induced by a microscopic dynamic of binary exchanges of masses between clusters. It models droplet formation, migration dynamics, and asset exchanges in various scientific and socio-economic contexts. It can also be viewed as a generalization of the continuous Smoluchowski equations. In this work, we show the existence and uniqueness of solutions for kernels with superlinear growth at infinity and singularity at the origin and show the non-existence of solutions for kernels with sufficiently rapid growth. The latter result is shown via the finite-time gelation and instantaneous gelation in the sense of moment blow-up.

math.AP↗

arXiv2025

Variational convergence for an irreversible exchange-driven stochastic particle system

We show the variational convergence of an irreversible Markov jump process describing a finite stochastic particle system to the solution of a countable infinite system of deterministic time-inhomogeneous quadratic differential equations known as the exchange-driven growth model, which has two conserved quantities. As a bounded perturbation of the reversible kernel, the variational formulation is a generalization of the gradient flow formulation of the reversible process and can be interpreted as the large deviation functional of the Markov jump process. As a consequence of the variational convergence result, we show the propagation of chaos of the Markov processes to the limiting equation and the $Γ$-convergence of the energy functional. The latter convergence is consistent with related results for reversible coagulation-fragmentation equations and reveals the connection of stochastic processes to the long-time condensation phenomena in the limit equation.

math.AP↗

arXiv2025

Convergence of a Stochastic Particle System to the Continuous Generalized Exchange-Driven Growth Model

The continuous generalized exchange-driven growth model (CGEDG) is a system of integro-differential equations describing the evolution of cluster mass under mass exchange. The rate of exchange depends on the masses of the clusters involved and the mass being exchanged. This can be viewed as both a continuous generalization of the exchange-driven growth model and a coagulation-fragmentation equation that generalizes the continuous Smoluchowski equation. Starting from a Markov jump process that describes a finite stochastic interacting particle system with exchange dynamics, we prove the weak law of large numbers for this process for sublinearly growing kernels in the mean-field limit. We establish the tightness of the stochastic process on a measure-valued Skorokhod space induced by the $1$-Wasserstein metric, from which we deduce the existence of solutions to the (CGEDG) system. The solution is shown to have a Lebesgue density under suitable assumptions on the initial data. Moreover, within the class of solutions with density, we establish the uniqueness under slightly more restrictive conditions on the kernel.

math.PR↗