# Workshop on Random Graphs, Combinatorial Limits, Stochastic Processes

### Description

The purpose of this workshop is to bring together experts and young scientists who will form WORKING GROUPS to SOLVE DIFFERENT PROBLEMS about RANDOM GRAPHS and RELATED MATHEMATICAL TOPICS IN A VERY BROAD SENSE.

The random graph is a fundamental object related to different fields. For example, graph limit theory is about understanding the large-scale structure of a graph, or in other words, understanding how a graph is different from a random graph. Statistical physics uses random graphs to model different physical matters and phase transitions on them. Group theory uses the fact that the Cayley-graph of a free group is locally equivalent to a random regular graph. There are other random structures such as random permutations which have analogous theory. In this broad area, it particularly often happens that a question is motivated by one field, but the best tools for solving it requires the tools of another field, and this is the reason why researchers from different related fields are very welcome.

We are asking the participants, especially the experts, to bring their best open problems and show the backgrounds of them.

The first day, 15 August, we plan a number of short talks for showing the problems and forming goups. In the later days, we will have one or maybe two talks in the mornings, and the rest of the day is dedicated to try to solve the problems in groups. (So the format will be similar to the very successful workshop “Interfaces of the Theory of Combinatorial Limits”)

**Talks:**

**Endre Csóka** (Rényi Institute): *Hoppen-Wormald type algorithms on graph limits***Łukasz Grabowski** (University of Leipzig):* Hypershallow digraphs***Jan Grebik** (Univ.of Warwick): *Local problems from the perspective of random processes and distributed algorithms***Eng Keat Hng** (The Czech Academy of Sciences): *Graph flip processes***Brice Huang** (MIT): *Max-cut in sparse graphs***Mark Kaufmann** (ETH Zurich): *Geometric constructions to large networks***Gábor Kun** (Rényi Institute):* Perfect matchings in graphings***Noela Müller** (Eindhoven University of Technology):* Partition function of random k-SAT problems***Zoltán Lóránt Nagy** (Eötvös Loránd University):* Bisection width, internal partitions, and r-degenerate graphs***Gábor Pete** (Rényi Institute):* Disconnected components of critical Erdős-Rényi random graphs*