## About

**A sound theory for analysing the complex behaviour of dynamic networks**

The aim of the EU-funded DYNASNET project is to engage leading experts in network science and graph theory to build a mathematically sound theory of dynamic networks.

## News

### László Lovász receives the Prima Primissima Award

### 2nd period overview

### Albert-László Barabási to receive the 2023 Julius Edgar Lilienfeld Prize from the The American Physical Society

## Latest Publications

### Random interlacement is a factor of i.i.d.

The random interlacement point process (introduced in [47], generalized in [ 50 ]) is a Poisson point process on the space of labeled doubly infinite nearest neighbour trajectories modulo time-shift on a transient graph G. We show that the random interlacement point process on any transient transitive graph G is a factor of i.i.d., i.e., it can be constructed from a family of i.i.d. random variables indexed by vertices of the graph via an equivariant measurable map.

### State-controlled epidemic in a game against a novel pathogen

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool.

### Locally common graphs

Goodman proved that the sum of the number of trianglesin a graph onnnodes and its complement is at least n3 / 24; in other words, this sum is minimized, asymptotically, by a random graph with edge density 1/2. Erdős conjectured that a similar inequality will hold for K4 in place of K3, but this was disproved by Thomason. But ananalogous statement does hold for some other graphs,which are called *common graphs*. Characterization ofcommon graphs seems, however, out of reach.

## Researchers

I work on graph limits of sequences of intermediate density

In spring 2022, I was helping to run the summer school Mathematics of Large Networks, organised by Márton Karsai, János Kertész, László Lovász, and Balázs Rath, as well as the summer school Graphs, Groups, Stochastic Processes that both took place in the Erdős Center within the semester of Large Networks and their Limits.

I am studying optimal transport related geometric properties of Markov processes with a particular emphasis on the Ollivier-Ricci curvature of graph limits.