In certain problems in a variety of applied probability settings (from probabilistic analysis of
algorithms to statistical physics), the central requirement is to solve a recursive distributional …

In this article we propose new methods for computing the asymptotic value for the logarithm
of the partition function (free energy) for certain statistical physics models on certain type of …

Let G (n, c/n) and Gr (n) be an n‐node sparse random graph and a sparse random r‐regular
graph, respectively, and let I (n, r) and I (n, c) be the sizes of the largest independent set in G …

We propose a new type of approximate counting algorithms for the problems of enumerating
the number of independent sets and proper colorings in low degree graphs with large girth …

The random assignment problem asks for the minimum-cost perfect matching in the
complete n× n bipartite graph 𝒦 nn with iid edge weights, say uniform on [0, 1]. In a …

Our model is a generalized linear programming relaxation of a much studied random K-SAT
problem. Specifically, a set of linear constraints on K variables is fixed. From a pool of n …

Given a recursive distributional equation (RDE) and a solution μ of it, we consider the tree
indexed invariant process called the recursive tree process (RTP) with marginal μ. We …

The assignment problem concerns finding the minimum-cost perfect matching in a complete
weighted n× n bipartite graph. Any algorithm for this classical question clearly requires Ω (n …

We provide a new characterisation of Duquesne and Le Gall's $\alpha $-stable tree,
$\alpha\in (1, 2] $, as the solution of a recursive distribution equation (RDE) of the form …

Chapters 2 and 3 of this thesis are based on a paper in preparation,“Partial observations of
a tree-indexed process”. We begin, in Chapter 1, with an introduction to the theory of …