Open problems within three topics in spatial networks: scale-invariance, the nearest unvisited vertex walk, and a toy model of 4X games

Combinatorial maps are a model of discrete geometry: they are surfaces made by gluing  polygons along their sides, or equivalently, graphs drawn on surfaces. In this talk, I'll focus on the study of

In this talk I will briefly recall the framework of local weak limits of finite graphs introduced by I. Benjamini and O. Schramm

Motivated by Krioukov et al.'s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a

This is a joint work with Agnes Backhausz et Balasz Szegedy. We define a natural notion of micro-state entropy...

A matching in a graph is a set of edges that do not share endpoints. Developing algorithms that find large matchings is an important problem. An algorithm is said to be online if it has to construct

We consider a sequence of Poisson cluster point processes on $R^d$: At step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c > 0$, and each cluster

Cost is a natural invariant associated to group actions and invariant point processes on symmetric spaces (such as Euclidean space and hyperbolic space). Informally, it measures how difficult it is to

The standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC)...

Consider two binary trees whose leaves are labelled from 1 to n.

It is known that the size of the largest common subtree...

A Markov decision process is called reversible if for every stationary Markov control strategy the resulting Markov chain is reversible.

The uniform measure on the set of all spanning trees of a finite graph is a classical object in probability.