11 citations · 28 across the 16 of their papers we have counts for
12 papers · 1 filter
IDS for subordinate Brownian motions in Poisson random environment on nested fractals
Hubert Balsam, Kamil Kaleta, Mariusz Olszewski +1
We establish the Lifshitz singularity of the integrated density of states (IDS) for random Schrödinger operators \[ H^ω = ϕ(-\mathcal{L}) + V^ω \] on planar unbounded nested fracta…
Bregman variation of semimartingales
Krzysztof Bogdan, Dominik Kutek, Katarzyna Pietruska-Pałuba
We define Bregman variation of semimartingales. We give its pathwise representation, Itô-type isometry for martingales, and applications to harmonic analysis.
Lifshitz tail for continuous Anderson models driven by Lévy operators
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We investigate the behavior near zero of the integrated density of states for random Schrödinger operators in , , where is a co…
Lifschitz tail for alloy-type models driven by the fractional Laplacian
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We establish precise asymptotics near zero of the integrated density of states for the random Schrödinger operators in for the full range of $…
Reflected Brownian motion on simple nested fractals
Kamil Kaleta, Mariusz Olszewski, Katarzyna Pietruska-Pałuba
We prove the existence of the reflected diffusion on a complex of an arbitrary size for a large class of planar simple nested fractals. Such a process is obtained as a folding proj…
The quenched asymptotics for nonlocal Schrödinger operators with Poissonian potentials
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We study the quenched long time behaviour of the survival probability up to time , of a symmetric Lévy process with jumps…
Lifschitz singularity for subordinate Brownian motions in presence of the Poissonian potential on the Sierpiński gasket
Kamil Kaleta, Katarzyna Pietruska-Pałuba
We establish the Lifschitz-type singularity around the bottom of the spectrum for the integrated density of states for a class of subordinate Brownian motions in presence of the no…
Lifschitz tail and sausage asymptotics for stable processes in the Poissonian environment on the Sierpinski gasket
Dorota Kowalska, Katarzyna Pietruska-Pałuba
We obtain the Lifschitz tail asymptotics for the integrated density of states of the subordinate stable processes on the Sierpiński gasket evolving among killing…
Integrated density of states for Poisson-Schrödinger perturbations of subordinate Brownian motions on the Sierpiński gasket
Kamil Kaleta, Katarzyna Pietruska-Paluba
We prove the existence of the integrated density of states for subordinate Brownian motions in presence of the Poissonian random potentials on the Sierpiński gasket.
Orlicz-space Hardy and Landau-Kolmogorov inequalities for Gaussian measures
Krzysztof Oleszkiewicz, Katarzyna Pietruska-Paluba
We prove Orlicz-space versions of Hardy and Landau-Kolmogorov inequalities for Gaussian measures on the n-dimensional Euclidean space.
Probabilistic characterisation of Besov-Lipschitz spaces on metric measure spaces
Katarzyna Pietruska-Pałuba
We give a probabilistic characterisation of the Besov-Lipschitz spaces on domains which support a Markovian kernel with appropriate exponential bounds. This extends…
Some function spaces related to the Brownian motion on simple nested fractals
Katarzyna Pietruska-Paluba
In this paper we identify the domain of the Dirichlet form associated with the Brownian motion on simple nested fractals with an integral Lipschitz space. This result generalizes s…