In this talk we will make a survey of how techniques of ``Grassmann
Calculus'', that is, integration of expressions involving
anticommuting variables, provide fermionic analogues of Gaussian
integration, Wick's Theorem and perturbative field theory. These
techniques are specially fruitful for describing certain combinatorial
models in Statistical Mechanics, namely $n=2$ Loop Models,...
We consider a Galton–Watson tree in which each node is independently marked, with a probability that depends on its number of offspring.
We give a complete picture of the local convergence of critical or subcritical marked Galton–Watson trees, conditioned on having a large number of marks.
In certain cases, the limit is a randomly marked tree with an infinite spine, known as the marked...
Networks appear naturally in a wide variety of context, including for example: biological networks , epidemics processes, electrical power grids and social networks. Most of those problems involve large dense graphs, that is graphs that have a large number of vertices and a number of edges that scales as the square of the number of vertices. Those graphs are too large to be represented...
