2 citations · 2 across the 5 of their papers we have counts for
5 papers
Expected perimeter and area of the convex hull of planar Brownian motion stopped upon exiting the unit disk
Rudi Mrazović, Hugo Panzo, Stjepan Šebek
We study the convex hull of planar Brownian motion run until the exit time from the unit disk. Our primary objectives are to compute the expected perimeter and expected area of thi…
Expected area of the star hull of planar Brownian motion and bridge
Hugo Panzo
We study the star hull of planar Brownian motion and bridge, and relate this random compact set to the more familiar convex and topological hulls. Roughly speaking, the star hull i…
A refinement of the Sylvester problem: Probabilities of combinatorial types
Zakhar Kabluchko, Hugo Panzo
Let be random points in . The classical Sylvester problem asks to determine the probability that the convex hull of these points, denoted by $P:=…
Sylvester's problem for random walks and bridges
Hugo Panzo
Consider a random walk in that starts at the origin and whose increment distribution assigns zero probability to any affine hyperplane. We solve Sylvester's problem…
Limit theorems for fixed point biased permutations avoiding a pattern of length three
Aksheytha Chelikavada, Hugo Panzo
We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. T…