Related papers: Character Expansion Methods for Matrix Models of D…

Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…

In the context of integrable partial difference equations on quad-graphs, we introduce the notion of open boundary reductions as a new means to construct discrete integrable mappings and their invariants. This represents an alternative to…

We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus…

Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed…

We study existence and universality of scaling limits for the eigenvalues of a random normal matrix, in particular at points on the boundary of the spectrum. Our approach uses Ward's equation, which is an identity satisfied by the 1-point…

Matrix functions are utilized to rewrite smooth spectral constrained matrix optimization problems as smooth unconstrained problems over the set of symmetric matrices which are then solved via the cubic-regularized Newton method. A…

In this paper we consider families of multiparametric $R$-matrices to make a systematic study of the boundary Yang-Baxter equations in order to discuss the corresponding families of multiparametric $K$-matrices. Our results are indeed…

In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to…

We compute an analogue of the Itzykson-Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson-Zuber diffusion equation method to the space of…

Given a finite connected graph $\Lambda$, the space of $SU(2)$ lattice gauge-fields on $\Lambda$, modulo gauge transformations, is a Lagrangian submanifold -- with mild singularities -- of the $SU(2)$ character variety (= phase-space of…

A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master…

We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…

This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…

A key property of neural networks is their capacity of adapting to data during training. Yet, our current mathematical understanding of feature learning and its relationship to generalization remain limited. In this work, we provide a…

In a previous work, we have been able to settle Jackiw's et al. chiral gauge theory for Dirac fermions in graphene in an N=1 supersymmetric framework, using a tau3-QED prescription, defined by means of a single pair of gauge charged…

In this paper, we address the problem of how a network of agents can collaboratively fit a linear model when each agent only ever has an arbitrary summand of the regression data. This problem generalizes previously studied…

A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…

Using matrix-model methods we study three different N=2 models: U(N) x U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find…

One of the main features of eigenvalue matrix models is that the averages of characters are again characters, what can be considered as a far-going generalization of the Fourier transform property of Gaussian exponential. This is true for…

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height…