23 citations · 72 across the 18 of their papers we have counts for
24 papers
Intertwining the Busemann process of the directed polymer model
Erik Bates, Wai-Tong Louis Fan, Timo Seppäläinen
We study the Busemann process and competition interfaces of the planar directed polymer model with i.i.d.\ weights on the vertices of the planar square lattice, in both the general…
Latent mutations in the ancestries of alleles under selection
Wai-Tong Louis Fan, John Wakeley
We consider a single genetic locus with two alleles and in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming t…
Patch formation driven by stochastic effects of interaction between viruses and defective interfering particles
Qiantong Liang, Johnny Yang, Wai-Tong Louis Fan +1
Defective interfering particles (DIPs) are virus-like particles that occur naturally during virus infections. These particles are defective, lacking essential genetic materials for…
Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions
Wai-Tong Louis Fan, Yifan Johnny Yang, Chaojie Yuan
The Togashi Kaneko model (TK model), introduced by Togashi and Kaneko in 2001, is a simple stochastic reaction network that displays discreteness-induced transitions between meta-s…
Detecting chaos in hurricane intensity
Chanh Kieu, Weiran Cai, Wai-Tong +1
Determining the maximum potential limit in the accuracy of hurricane intensity prediction is important for operational practice. Using the phase-space reconstruction method for hur…
Hitting Time of Rapid Intensification Onset in Hurricane-like Vortices
Wai-Tong Louis Fan, Chanh Kieu, Dimitrios Sakellariou +1
Predicting tropical cyclone (TC) rapid intensification (RI) is an important yet challenging task in current operational forecast due to our incomplete understanding of TC nonlinear…
Impossibility of phylogeny reconstruction from -mer counts
Wai-Tong Louis Fan, Brandon Legried, Sebastien Roch
We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity,…
Modeling Atmospheric Data and Identifying Dynamics: Temporal Data-Driven Modeling of Air Pollutants
Javier Rubio-Herrero, Carlos Ortiz Marrero, Wai-Tong Louis Fan
Atmospheric modeling has recently experienced a surge with the advent of deep learning. Most of these models, however, predict concentrations of pollutants following a data-driven…
Three-dimensional shear driven turbulence with noise at the boundary
Wai-Tong Louis Fan, Michael Jolly, Ali Pakzad
We consider the incompressible 3D Navier-Stokes equations subject to a shear induced by noisy movement of part of the boundary. The effect of the noise is quantified by upper bound…
Impossibility of consistent distance estimation from sequence lengths under the TKF91 model
Wai-Tong Louis Fan, Brandon Legried, Sebastien Roch
We consider the problem of distance estimation under the TKF91 model of sequence evolution by insertions, deletions and substitutions on a phylogeny. In an asymptotic regime where…
Correlation function methods for a system of annihilating Brownian particles
Wai-Tong Louis Fan
In this expository note we highlight the correlation function method as a unified approach in proving both hydrodynamic limits and fluctuation limits for reaction diffusion particl…
Wave propagation for reaction-diffusion equations on infinite random trees
Wai-Tong Louis Fan, Wenqing Hu, Grigory Terlov
The asymptotic wave speed for FKPP type reaction-diffusion equations on a class of infinite random metric trees are considered. We show that a travelling wavefront emerges, provide…
Joint distribution of Busemann functions in the exactly solvable corner growth model
Wai-Tong Louis Fan, Timo Seppäläinen
The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models.…
Stochastic PDEs on graphs as scaling limits of discrete interacting systems
Wai-Tong Louis Fan
Stochastic partial differential equations (SPDE) on graphs were introduced by Cerrai and Freidlin [Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 865-899]. This class of stochas…
Statistically consistent and computationally efficient inference of ancestral DNA sequences in the TKF91 model under dense taxon sampling
Wai-Tong Louis Fan, Sebastien Roch
In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and…
Necessary and sufficient conditions for consistent root reconstruction in Markov models on trees
Wai-Tong Louis Fan, Sebastien Roch
We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root…
Large Deviations for Brownian Particle Systems with Killing
Amarjit Budhiraja, Wai-Tong Louis Fan, Ruoyu Wu
Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a co…
Uniform in Time Interacting Particle Approximations for Nonlinear Equations of Patlak-Keller-Segel type
Amarjit Budhiraja, Wai-Tong Louis Fan
We study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified…
Genealogies in Expanding Populations
Rick Durrett, Wai-Tong Louis Fan
The goal of this paper is to prove rigorous results for the behavior of genealogies in a one-dimensional long range biased voter model introduced by Hallatschek and Nelson [25]. Th…
Fluctuation limit for interacting diffusions with partial annihilations through membranes
Zhen-Qing Chen, Wai-Tong Louis Fan
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and est…
Discrete approximations to local times for reflected diffusions
Wai-Tong Louis Fan
We propose a discrete analogue for the boundary local time of reflected diffusions in bounded Lipschitz domains. This discrete analogue, called the discrete local time, can be effe…
Functional central limit theorem for Brownian particles in domains with Robin boundary condition
Zhen-Qing Chen, Wai-Tong Louis Fan
We rigorously derive non-equilibrium space-time fluctuation for the particle density of a system of reflected diffusions in bounded Lipschitz domains in . The particle…
Systems of interacting diffusions with partial annihilation through membranes
Zhen-Qing Chen, Wai-Tong Fan
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface . This system can be used…
Hydrodynamic Limits and Propagation of Chaos for Interacting Random Walks in Domains
Zhen-Qing Chen, Wai-Tong Louis Fan
A new non-conservative stochastic reaction-diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in t…