19.VI.2024 (Blackboard, room 329)
Amir Dembo, Stanford University, USA
"Limit law for Brownian cover time of the two-dimensional torus"
Abstract: Consider the time \(C(r)\) it takes a Brownian motion to come within distance \(r\) of every point in the two-dimensional torus of area one. I will discuss the key ideas in a joint work with Jay Rosen and Ofer Zeitouni, showing that as \(r\) goes to zero, the square-root of \(C(r)\), minus an explicit non-random centering \(m(r)\), converges in distribution to a randomly shifted Gumbel law.
Amir Dembo, Stanford University, USA
"Limit law for Brownian cover time of the two-dimensional torus"
Abstract: Consider the time \(C(r)\) it takes a Brownian motion to come within distance \(r\) of every point in the two-dimensional torus of area one. I will discuss the key ideas in a joint work with Jay Rosen and Ofer Zeitouni, showing that as \(r\) goes to zero, the square-root of \(C(r)\), minus an explicit non-random centering \(m(r)\), converges in distribution to a randomly shifted Gumbel law.
Everyone is cordially invited!
B. Kołodziejek, W. Matysiak, K. Szpojankowski, J. Wesołowski