Louigi Addario-Berry

Minima in branching random walks

Given a branching random walk, let

Vertex colouring edge partitions

M_n

On combinatorial testing problems

be the minimum position of any member of the

Vertex-Colouring Edge-Weightings

n

Bisimplicial vertices in even-hole-free graphs

th generation. We calculate

Ancestral maximum likelihood of evolutionary trees is hard.

\\mathbfEM_n

The scaling limit of the minimum spanning tree of the complete graph

to within O(1) and prove exponential tail bounds for

The scaling limit of random simple triangulations and random simple quadrangulations

\\mathbfP{|M_n-\\mathbfEM_n|>x}

Sub-Gaussian tail bounds for the width and height of conditioned Galton–Watson trees

, under quite general conditions on the branching random walk. In particular, together with work by Bramson [Z. Wahrsch. Verw. Gebiete 45 (1978) 89―108], our results fully characterize the possible behavior of

Ballot Theorems, Old and New

\\mathbf EM_n