A common obstruction to efficient sampling from high-dimensional distributions with Markov
chains is the multimodality of the target distribution because they may get trapped far from …

There are a number of well‐known problems and conjectures about partitioning graphs to
satisfy local constraints. For example, the majority colouring conjecture of Kreutzer, Oum …

Resolving a conjecture of Füredi from 1988, we prove that with high probability, the random
graph $\mathbb {G}(n, 1/2) $ admits a friendly bisection of its vertex set, ie, a partition of its …

We study the zero-temperature stochastic Ising model on some connected planar quasi-
transitive graphs, which are invariant under rotations and translations. The initial spin …

We study the metastable minima of the Curie–Weiss Potts model with three states, as a
function of the inverse temperature, and for arbitrary vector-valued external fields. Extending …

The zero-temperature Ising model is known to reach a fully ordered ground state in
sufficiently dense random graphs. In sparse random graphs, the dynamics gets absorbed in …

We consider the complexity of random ferromagnetic landscapes on the hypercube {±\, 1\}^
N±1 N given by Ising models on the complete graph with iid non-negative edge-weights …

In this thesis, we examine the question of fixation for zero-temperature stochastic Ising
model on some connected quasi-transitive graphs. The initial spin con figuration is …

We study the predictability of zero-temperature Glauber dynamics in various models of
disordered ferromagnets. This is analyzed using two independent dynamical realizations …

In this thesis we are investigating a time-evolved version of the symmetric mean-field Potts
model. It is our goal to understand the critical parameters (both temperature and time) for …