The next Kutszem will be at the usual place and time.

Speaker: Neeladri Maitra (Eindhoven)

Title: Long-range competition on the complete graph

Abstract: In this talk we will consider a competition between two growth models with long-range correlations on the complete graph.
The complete graph is viewed as embedded on the torus $\T_n^d$ of size $n$ in dimensions $d$, by including all the non-nearest neighbor edges,
and from two sources two first-passage percolation (FPP) processes start flowing on the graph and compete to cover the sites. The FPP
processes we consider are long-range first-passage percolation processes, as studied by Chatterjee and Dey (https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21571),
in the instantaneous percolation regime (a regime of low dependence on the underlying geometry), with different rates and different long-range
parameters, that we allow to depend on $n$. We will see interesting phase transitions in the size of the weaker FPP type, depending on the
rate of the stronger type. We will discuss the key techniques and ideas, some particular examples, and some interesting open problems.
(Joint work with Bas Lodewijks)