27.05.2026
Piotr Śniady, Instytut Matematyczny PAN
"Exact formulas for coalescing particle systems"
Abstract: Consider particles on the integers or the real line that perform random walks and coalesce when they collide. The classical Karlin-McGregor theorem gives determinantal formulas for non-colliding particles on the line, but coalescence reduces the particle count and breaks the square matrix structure. Our approach: at each collision, a ghost particle continues along an independent path, preserving the total particle count and yielding determinantal formulas for any skip-free process. Summing out ghost positions recovers the original ghost-free system. Applications include Rayleigh gap distributions between surviving particles, a Pfaffian point process structure for basin boundaries (extending Tribe-Zaboronski and Garrod-Poplavskyi-Tribe-Zaboronski), and a central limit theorem.
Additional materials available at psniady.impan.pl/kmg
Based on joint work with Ákos Urbán.
Piotr Śniady, Instytut Matematyczny PAN
"Exact formulas for coalescing particle systems"
Abstract: Consider particles on the integers or the real line that perform random walks and coalesce when they collide. The classical Karlin-McGregor theorem gives determinantal formulas for non-colliding particles on the line, but coalescence reduces the particle count and breaks the square matrix structure. Our approach: at each collision, a ghost particle continues along an independent path, preserving the total particle count and yielding determinantal formulas for any skip-free process. Summing out ghost positions recovers the original ghost-free system. Applications include Rayleigh gap distributions between surviving particles, a Pfaffian point process structure for basin boundaries (extending Tribe-Zaboronski and Garrod-Poplavskyi-Tribe-Zaboronski), and a central limit theorem.
Additional materials available at psniady.impan.pl/kmg
Based on joint work with Ákos Urbán.
Everyone is cordially invited!
B. Kołodziejek, W. Matysiak, K. Szpojankowski, J. Wesołowski