4 papers
HyperLogLog for probabilists
Lucas Gerin
HyperLogLog is a now classic probabilistic algorithm that provides an approximation of the number of distinct elements in a massive dataset, using only one pass over the data. In t…
Longest increasing subsequences for distributions with atoms, and an inhomogeneous Hammersley process
Anne-Laure Basdevant, Lucas Gerin, Maxime Marivain
A famous result by Hammersley and Versik-Kerov states that the length of the longest increasing subsequence among iid continuous random variables grows like .…
Maximal Entropy Random Walks in Z: Random and non-random environments
Duboux Thibaut, Lucas Gerin, Yoann Offret
The Maximal Entropy Random Walk (MERW) is a natural process on a finite graph, introduced a few years ago with motivations from theoretical physics. The construction of this proces…
From Hammersley's lines to Hammersley's trees
Anne-Laure Basdevant, Lucas Gerin, Jean-Baptiste Gouere +1
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. Th…