Related papers: Integrability Condition in the Statistical Model a…
The analytic method for deriving the equation of state of a cell fluid model in the region above the critical temperature ($T \geqslant T_\text{c}$) is elaborated using the renormalization group transformation in the collective variables…
In this paper we compute the superconformal index of 2d (2,2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes…
Let HH_{ab}(H) be the equivariant Hilbert scheme parametrizing the zero dimensional subschemes of the affine plane k^2, fixed under the one dimensional torus T_{ab}={(t^{-b},t^a), t\in k^*} and whose Hilbert function is H. This Hilbert…
For a system near a second order phase transition, the probability distribution for the order parameter can be given a finite size scaling form. This fact is used to compare the finite temperature phase transition for the Wilson lines in…
The hyperbolic model (HM) time integration scheme tackles parabolic problems by adding a small artificial second order time derivative term. Described by Samarskii in his 1971 book, the scheme reappeared as the generalized Du Fort-Frankel…
We formulate a division problem for a class of overdetermined systems introduced by L. H{\"o}rmander, and establish an effective divisibility criterion. In addition, we prove a coherence theorem which extends Nadel's coherence theorem from…
We derive conditions for $L_2$ differentiability of generalized linear models with error distributions not necessarily belonging to exponential families, covering both cases of stochastic and deterministic regressors. These conditions…
The Higgs inflation scenario is an approach to realize the cosmic inflation, where the Higgs boson plays a role of the inflaton. In the minimal model, it would be difficult to satisfy theoretical constraints from vacuum stability and…
Solutions to elliptic equations often exhibit higher regularity properties such as \emph{higher integrability}. That is, for instance, a solution $u$ to a system that a priori only satisfies $ u \in W^{1,r}$ is more regular and even in the…
We consider the integrable XXZ model with special open boundary conditions that renders its Hamiltonian ${SU(2)}_q$ symmetric, and the one-dimensional quantum Ising model with four different boundary conditions. We show that for each…
The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the…
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We…
This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference…
In this paper we study generalised Ising Glauber models with inflow of informa- tion in one dimension and derive expressions for the exit probability using well established analytical methods. The analytical expressions agree very well with…
We establish nonparametric identification in a class of so-called index models using a novel approach that relies on general topological results. Our proof strategy requires substantially weaker conditions on the functions and distributions…
In a pedagogical but exhaustive manner, this survey reviews the main results on input-to-state stability (ISS) for infinite-dimensional systems. This property allows estimating the impact of inputs and initial conditions on both the…
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational…
Input-to-state stability (ISS) allows estimating the impact of inputs and initial conditions on both the intermediate values and the asymptotic bound on the solutions. ISS has unified the input-output and Lyapunov stability theories and is…
We present the exact solution of the Richardson-Gaudin models associated with the SU(3) Lie algebra. The derivation is based on a Gaudin algebra valid for any simple Lie algebra in the rational, trigonometric and hyperbolic cases. For the…
The Peierls argument is a mathematically rigorous and intuitive method to show the presence of a non-vanishing spontaneous magnetization in some lattice models. This argument is typically explained for the $D=2$ Ising model in a way which…