Related papers: Character expansion method for the first order asy…
The strong-coupling character expansion of lattice models is reanalyzed in the perspective of its complete algorithmization. The geometric problem of identifying, counting, and grouping together all possible contributions is disentangled…
We characterize asymptotic collective behaviour of rectangular random matrices, the sizes of which tend to infinity at different rates: when embedded in a space of larger square matrices, independent rectangular random matrices are…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
In this paper we study multi-matrix models whose potentials are perturbations of the quadratic potential associated with independent GUE random matrices. More precisely, we compute the free energy and the expectation of the trace of…
High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality $p$ tends to $\infty$ as the sample size $n$ increases.…
A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite sub-matrices of an infinite nonnegative…
A late time asymptotic perturbative analysis of curvature coupled complex scalar field models with accelerated cosmological expansion is carried out on the level of formal power series expansions. For this, algebraic analogues of the…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping,…
The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger…
The convolution of indicators of two conjugacy classes on the symmetric group S_q is usually a complicated linear combination of indicators of many conjugacy classes. Similarly, a product of the moments of the Jucys--Murphy element involves…
We enumerate the connected graphs that contain a number of edges growing linearly with respect to the number of vertices. So far, only the first term of the asymptotics and a bound on the error were known. Using analytic combinatorics, ie…
Determining the Shannon capacity of graphs is a long-standing open problem in information theory, graph theory and combinatorial optimization. Over decades, a wide range of upper and lower bound methods have been developed to analyze this…
This paper develops a method to carry out the large-$N$ asymptotic analysis of a class of $N$-dimensional integrals arising in the context of the so-called quantum separation of variables method. We push further ideas developed in the…
We compute a rigorous asymptotic expansion of the energy of a point defect in a 1D chain of atoms with second neighbour interactions. We propose the Confined Lennard-Jones model for interatomic interactions, where it is assumed that nearest…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…
For a $(3+1)$-dimensional generalization of the Schwinger model, we compute the interaction energy between two test charges. The result shows that the static potential profile contains a linear term leading to the confinement of probe…
We show how to expand the free energy of a matrix model coupled to arbitrary matter in powers of the matter coupling constant. Concentrating on $\nu$ uncoupled Ising models---which have central charge $\nu/2$---we work out the expansion to…
Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing…
The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the 't Hooft expansion for matrix integral, these solutions are described by…