1 citations · 1 across the 9 of their papers we have counts for
9 papers
Dirichlet metric measure spaces: spectrum, irreducibility, and small deviations
Marco Carfagnini, Maria Gordina, Alexander Teplyaev
We show that for ultracontractive irreducible Dirichlet metric measure spaces, the Dirichlet spectrum is discrete for a restriction to any connected open set without any assumption…
Onsager-Machlup functional for loop measures
Marco Carfagnini, Yilin Wang
We relate two ways to renormalize the Brownian loop measure on the Riemann sphere. One by considering the Brownian loop measure on the sphere minus a small disk, known as the norma…
Spectral gap bounds on H-type groups
Marco Carfagnini, Maria Gordina
In this note we provide bounds on the spectral gap for the Dirichlet sub-Laplacians on -type groups. We use probabilistic techniques and in particular small deviations of the co…
Dirichlet sub-Laplacians on homogeneous Carnot groups: spectral properties, asymptotics, and heat content
Marco Carfagnini, Maria Gordina
We consider sub-Laplacians in open bounded sets in a homogeneous Carnot group and study their spectral properties. We prove that these operators have a pure point spectrum, and pro…
An application of the Gaussian correlation inequality to the small deviations for a Kolmogorov diffusion
Marco Carfagnini
We consider an iterated Kolmogorov diffusion of step . The small ball problem for is solved by means of the Gaussian correlation inequality. We also prove Chung'…
A functional Law of the Iterated Logarithm for weakly hypoelliptic diffusions at time zero
Marco Carfagnini, Juraj Foldes, David P. Herzog
We study the almost sure behavior of solutions of stochastic differential equations (SDEs) as time goes to zero. Our main general result establishes a functional law of the iterate…
On the Support of a hypoelliptic diffusion on the Heisenberg group
Marco Carfagnini
We provide an elementary proof of the support of the law of a hypoelliptic Brownian motion on the Heisenberg group . We consider a control norm associated to left-invar…
Small deviations and Chung's law of iterated logarithm for a hypoelliptic Brownian motion on the Heisenberg group
Marco Carfagnini, Maria Gordina
A small ball problem and Chung's law of iterated logarithm for a hypoelliptic Brownian motion in Heisenberg group are proven. In addition, bounds on the limit in Chung's law are es…
On the Onsager-Machlup functional for the Brownian motion on the Heisenberg group
Marco Carfagnini, Maria Gordina
Onsager-Machlup functionals are used to describe the dynamics of a continuous stochastic process. For a stochastic process taking values in a Riemannian manifold, they have been st…