James H. Nolen

Journal article Quarterly of Applied Mathematics · January 1, 2024 Featured Work We study the mixing time of a random walk on the torus, alternated with a Lebesgue measure preserving Bernoulli map. Without the Bernoulli map, the mixing time of the random walk alone is O(1/ε2), where ε is the step size. Our main results show that for a ... Full text Cite

The Fleming-Viot Process with McKean-Vlasov Dynamics

Journal article Electronic Journal of Probability · August 3, 2022 Featured Work The Fleming-Viot particle system consists of N identical particles diffusing in a domain U⊂Rd. Whenever a particle hits the boundary ∂U, that particle jumps onto another particle in the interior. It is known that this system provides a particle representat ... Full text Link to item Cite

Brownian bees in the infinite swarm limit

Journal article Annals of Probability · 2022 Featured Work Full text Link to item Cite

A free boundary problem arising from branching Brownian motion with selection

Journal article Transactions of the American Mathematical Society · May 18, 2021 Featured Work We study a free boundary problem for a parabolic partial differential equation in which the solution is coupled to the moving boundary through an integral constraint. The problem arises as the hydrodynamic limit of an interacting pa ... Full text Cite

Quantitative propagation of chaos in a bimolecular chemical reaction-diffusion model

Journal article SIAM Journal on Mathematical Analysis · January 1, 2020 Featured Work We study a stochastic system of N interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle i carries two attributes: the spatial location Xit ∈ Td, and the type [I]i Full text Cite

Refined long-time asymptotics for Fisher–KPP fronts

Journal article Communications in Contemporary Mathematics · November 2019 Featured Work We study the one-dimensional Fisher–KPP equation, with an initial condition [Formula: see text] that coincides with the step function except on a compact set. A well-known result of Bramson in [Maximal displacement of branching Brownian motion, Co ... Full text Cite

Ratiometric GPCR signaling enables directional sensing in yeast.

Journal article PLoS Biol · October 2019 Featured Work Accurate detection of extracellular chemical gradients is essential for many cellular behaviors. Gradient sensing is challenging for small cells, which can experience little difference in ligand concentrations on the up-gradient and down-gradient sides of ... Full text Open Access Link to item Cite

Scaling limit of the Stein variational gradient descent: The mean field regime

Journal article SIAM Journal on Mathematical Analysis · January 1, 2019 Featured Work We study an interacting particle system in Rd motivated by Stein variational gradient descent [Q. Liu and D. Wang, Proceedings of NIPS, 2016], a deterministic algorithm for approximating a given probability density with unknown normalization bas ... Full text Cite