4 papers · 1 filter
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.…