Related papers: A challenge in enumerative combinatorics: The grap…
The concern of this paper is a famous combinatorial formula known under the name "exponential formula". It occurs quite naturally in many contexts (physics, mathematics, computer science). Roughly speaking, it expresses that the exponential…
We give a full account of the Numerical Stochastic Perturbation Theory method for Lattice Gauge Theories. Particular relevance is given to the inclusion of dynamical fermions, which turns out to be surprisingly cheap in this context. We…
We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions…
Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of…
This paper investigates the relationship between categorical entropy and von Neumann entropy of quantum lattices. We begin by studying the von Neumann entropy, proving that the average von Neumann entropy per site converges to the logarithm…
This paper aims to recall some of the main contributions of Roberto Petronzio to physics, with a particular regard to the period we have been working together. His seminal contributions cover an extremely wide range of topics: the…
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
Matchings were among the earliest motivations for graph theory. They subsequently remained a central goal, inspiring the development of new tools that went well beyond problems directly concerning matchings. These tools proved widely…
The comparison of structural analogies between the energy-momentum tensors in general relativity and in a gauge theory of Yang-Mills type is tentatively extended to lattice physics. These considerations are guiding to a new lattice model…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
Various different random graph models have been proposed in which the vertices of the graph are seen as members of a metric space, and edges between vertices are determined as a function of the distance between the corresponding metric…
Many enumeration problems in combinatorics, including such fundamental questions as the number of regular graphs, can be expressed as high-dimensional complex integrals. Motivated by the need for a systematic study of the asymptotic…
This is a review to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific. It showcases a selection of contributions from the spin glass community at…
These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This…
We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to…
Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a…
Let $G=(V,E,w)$ be a finite, connected graph with weighted edges. We are interested in the problem of finding a subset $W \subset V$ of vertices and weights $a_w$ such that $$ \frac{1}{|V|}\sum_{v \in V}^{}{f(v)} \sim \sum_{w \in W}{a_w…
Many-body perturbation theory (MBPT) is widely used in quantum physics, chemistry, and materials science. At the heart of MBPT is the Feynman diagrammatic expansion, which is, simply speaking, an elegant way of organizing the…