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Ioannis Papageorgiou

Publications and source records attributed to Ioannis Papageorgiou.

25 records · Page 2Linked to original sources
arXiv2018

Log-Sobolev inequalities for infinite-dimensional Gibbs measures with non-quadratic interactions

We focus on the log-Sobolev inequality for spin systems on the lattice with interactions of higher order than quadratic. We show that if the one-dimensional single-site measure with boundaries satisfies the log-Sobolev inequality uniformly in the boundary conditions then the infinite-dimensional Gibbs measure also satisfies the inequality under appropriate conditions on the phase and the interactions.

math.FA↗
arXiv2017

The log-Sobolev inequality with quadratic interactions

We assume one site measures without a boundary $e^{-ϕ(x)}dx/Z$ that satisfy a log-Sobolev inequality. We prove that if these measures are perturbed with quadratic interactions, then the associated infinite dimensional Gibbs measure on the lattice always satisfies a log-Sobolev inequality. Furthermore, we present examples of measures that satisfy the inequality with a phase that goes beyond convexity at infinity.

math.FA↗
arXiv2011

Logarithmic Sobolev inequalities for infinite dimensional Hörmander type generators on the Heisenberg group

The Heisenberg group is one of the simplest sub-Riemannian settings in which we can define non-elliptic Hörmander type generators. We can then consider coercive inequalities associated to such generators. We prove that a certain class of nontrivial Gibbs measures with quadratic interaction potential on an infinite product of Heisenberg groups satisfy logarithmic Sobolev inequalities.

math.FA↗
arXiv2010

A note on the Modified Log-Sobolev inequality

A criterion is presented for the Modified Logarithmic Sobolev inequality on metric measure spaces. The criterion based on U-bound inequalities introduced by Hebisch and Zegarlinski allows to show the inequality for measures that go beyond log-concavity.

math.FA↗
arXiv2010

Concentration inequalities for Gibbs measures

We are interested in Sobolev type inequalities and their relationship with concentration properties on higher dimensions. We consider unbounded spin systems on the d-dimensional lattice with interactions that increase slower than a quadratic. At first we assume that the one site measure satisfies a Modified log-Sobolev inequality with a constant uniformly on the boundary conditions and we determine conditions so that the infinite dimensional Gibbs measure satisfies a concentration as well as a Talagrand type inequality. Then a Modified Log-Sobolev type concentration property is obtained under weaker conditions referring to the Log-Sobolev inequalities for the boundary free measure.

math.PR↗
arXiv2010

The Logarithmic Sobolev Inequality in Infinite dimensions for Unbounded Spin Systems on the Lattice with non Quadratic Interactions

We are interested in the Logarithmic Sobolev Inequality for the infinite volume Gibbs measure with no quadratic interactions. We consider unbounded spin systems on the one dimensional Lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one dimensional single-site measure with boundaries satisfies the Log-Sobolev inequality uniformly on the boundary conditions and we determine conditions under which the Log-Sobolev Inequality can be extended to the infinite volume Gibbs measure.

math.FA↗