Related papers: Exponential frames and Riesz sequences at the crit…
It is now well known that sparse or compressible vectors can be stably recovered from their low-dimensional projection, provided the projection matrix satisfies a Restricted Isometry Property (RIP). We establish new implications of the RIP…
The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method. The finite-size crossover in impure films has been considered on the basis of the…
The purpose of this work is twofold. First, we aim to extend for $0<s<1$ the results of one of the authors about equilibrium measures in the real axis in external fields created by point-mass charges for the case of logarithmic potentials…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…
We prove that for any convex polytope $\Omega \subset \mathbb{R}^d$ which is centrally symmetric and whose faces of all dimensions are also centrally symmetric, there exists a Riesz basis of exponential functions in the space $L^2(\Omega)$.…
Inspired by a recent work about distribution frames, the definition of multiplier operator is extended in the rigged Hilbert spaces setting and a study of its main properties is carried on. In particular, conditions for the density of…
The edge of a quantum critical system can exhibit multiple distinct types of boundary criticality. We use a numerical real-space renormalization group (RSRG) to study the boundary criticality of a 2d quantum Ising model with random exchange…
It is well known that a sequence in a Hilbert space is a Riesz basis if and only if it is a complete Bessel sequence with biorthogonal sequence which is also a complete Bessel sequence. Here we prove that the completeness of one (any one)…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…
A one-parameter family of point processes describing the distribution of the critical points of the characteristic polynomial of large random Hermitian matrices on the scale of mean spacing is investigated. Conditionally on the Riemann…
A detailed study of critical spreading in the one-dimensional pair contact process is performed using a recently devised reweighting method. The results confirm the validity of a generalized hyperscaling relation among the (nonuniversal)…
In this paper we investigate iteration of maps on lattices and the corresponding polynomial-like iterative equation. Since a lattice need not have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point…
This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…
We establish the local wellposedness of different type of solutions the system with different types of initial data. We find there exists a critical exponents line in space dimension 3 and critical exponents point in space dimension 4. We…
Given a domain $\Omega\subset\Bbb R^d$ with positive and finite Lebesgue measure and a discrete set $\Lambda\subset \Bbb R^d$, we say that $(\Omega, \Lambda)$ is a {\it frame spectral pair} if the set of exponential functions $\mathcal…
Here we prove critical exponents for Random Connections Models (RCMs) with random marks. The vertices are given by a marked Poisson point process on $\mathbb{R}^d$ and an edge exists between any pair of vertices independently with a…
In this paper, we study the weak compactness of the set of conformal metrics in any Riemann surface without boundary whose Calabi energy and area are uniformly bounded. We prove that for any sequence of such metrics, there alwasy exists a…