Related papers: Focusing Gibbs measures with harmonic potential
We show that the emerging field of discrete differential geometry can be usefully brought to bear on crystallization problems. In particular, we give a simplified proof of the Heitmann-Radin crystallization theorem (R. C. Heitmann, C.…
On the space of Ising configurations on the 2-d square lattice, we consider a family of non Gibbsian measures introduced by using a pair Hamiltonian, depending on an additional inertial parameter $q$. These measures are related to the usual…
Unconditional guaranteed lower and upper eigenvalue bounds are mandatory for the understanding of the Schr\"odinger eigenvalue spectrum and its spectral gaps. While upper eigenvalue bounds are naturally induced by conforming…
The multifractal formalism for measures hold whenever the existence of corresponding Gibbs-like measures supported on the singularities sets holds. In the present work we tried to relax such a hypothesis and introduce a more general…
In the context of non-Gaussian analysis, Schneider [27] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations were constructed (see, for example, [25], [6], [7], [8]).…
Motivated by applications to quantum field theory we consider Gibbs measures for which the reference measure is Wiener measure and the interaction is given by a double stochastic integral and a pinning external potential. In order properly…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular…
For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…
The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions…
It is believed that the canonical gravitational partition function $Z$ associated to the classical Boltzmann-Gibbs (BG) distribution $\frac {e^{-\beta H}} {{\cal Z}}$ cannot be constructed because the integral needed for building up $Z$…
We aim this paper to develop the classical lattice models with unbounded spin to the case of non-quadratic polynomial interaction. We demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the…
We establish bounds for the measure of deviation sets associated to continuous observables with respect to not necessarily invariant weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of…
We are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of…
This work concerns superharmonic perturbations of a Gaussian measure given by a special class of positive weights in the complex plane of the form $w(z) = \exp(-|z|^2 + U^{\mu}(z))$, where $U^{\mu}(z)$ is the logarithmic potential of a…
We discuss the problem of unitarity for Yang-Mills theory in the Landau gauge with a mass term a la Stueckelberg. We assume that the theory (non-renormalizable) makes sense in some subtraction scheme (in particular the Slavnov-Taylor…
For the special case of compact QED in (2+1) dimensions, we calculate the non-Gaussian vacuum wave-functional to second order in the monopole fugacity and obtain the effective photon mass. Our method presents some hope for understanding the…
The present paper is devoted to the semiclassical analysis of linear Schr\"odinger equations from a Gabor frame perspective. We consider (time-dependent) smooth Hamiltonians with at most quadratic growth. Then we construct higher order…
We prove that five characterizations of Gibbs measures for H\"{o}lder potentials on topologically mixing subshifts of finite type are equivalent: the Jacobian condition, the classical cylinder-based Gibbs property, the eigenmeasure of the…
This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces,…