5 papers
Pfaffian structure of basin walls for coalescing particles
Piotr Śniady
Coalescing particles on a line merge when they meet. As they do, their basins of attraction merge and the walls between basins disappear. If every site is initially occupied, these…
Coalescing random walks via the coalescence determinant
Piotr Śniady
When identical particles on a line collide, they merge and continue as one. Exact determinantal formulas have long been available for particles conditioned never to collide, but co…
Determinant and Pfaffian formulas for particle annihilation
Piotr Śniady
We consider systems of particles on a line in which colliding particles annihilate each other and vanish. Computing exact annihilation probabilities is difficult because every coll…
Exact determinant formulas for coalescing particle systems
Piotr Śniady, Ákos Urbán
When particles on a line collide, they may coalesce into one. Such systems arise in the voter model, where boundaries between opinion clusters perform coalescing random walks, and…
Modulus of continuity of Kerov transition measure for continual Young diagrams
Piotr Śniady
The transition measure is a foundational concept introduced by Sergey Kerov to represent the shape of a Young diagram as a centered probability measure on the real line. Over a per…