Work in preparation (June 2021); extension for the case and the case.
In parallel, I'm interested in the rigidites of random point processes, such as number-rigidities, fluctuations reductions, hyperuniformity, and the possible links between these notions. There are different ways in which point processes in can exhibit a stronger order than the totally chaotic Poisson process; hyperuniformity is when the (random) number of points falling in a large domain of radius has a reduced variance, that is, when
In this survey, I try to give a mathematical overview of this rich domain. Topics: the Fourier caracterization of hyperuniformity, the fluctuation scale, the links with number-rigidity and maximal rigidity for stealthy processes, the example of pertubed lattices.
Here is a version of this survey. It's still work in progress.
Hyperuniformity survey (may 2021: added a paragraph on the zeroes of the GEF)
Joint work with Charles Bordenave.
Arxiv link – Published in Journal of Combinatorial Theory (series B).
This is a short note on a generalization of the Erdös-Gallai theorem on graphical sequences.