Diluted mean-field models are spin systems whose geometry of interactions is induced by a
sparse random graph or hypergraph. Such models play an eminent role in the statistical …

We verify a key component of the replica symmetry breaking hypothesis put forward in the
physics literature (Mézard and Montanari in Information, physics and computation. Oxford …

We present a unifying approach to studying the replica symmetric solution in general diluted
spin glass models on random $ p $-uniform hypergraphs with sparsity parameter $\alpha …

Let $\hom (H, G) $ denote the number of homomorphisms from a graph $ H $ to a graph $ G
$. Sidorenko's conjecture asserts that for any bipartite graph $ H $, and a graph $ G $ we …

We study Gibbs distributions of spins taking values in a general compact Polish space,
interacting via a pair potential along the edges of a generalized random graph with a given …

Im ersten Kapitel studieren wir Gibbs' sche Modelle auf Baumgraphen, welche unter
Höhenshifts invariant sind und einen nicht-kompakten lokalen Zustandsraum aufweisen. Es …

The goal of this book is to give an account into the study of counting various objects in
sparse graphs. The main objects whose study will run through the book are matchings …

This PhD thesis deals with two different types of questions on random graph and random
hypergraph structures. One part is about the proof of the existence and the determination of …