K. Kaleta

activity

20092026

most citedEstimates of transition densities and their derivatives for jump Lévy processes

68 citations · 248 across the 33 of their papers we have counts for

collaborators

37 papers

math.CA2026

Critical discrete Hardy inequalities in $L^{p}$

Krzysztof Bogdan, Shubham Gupta, Kamil Kaleta +1

We establish ground-state representations and critical Hardy inequalities in the discrete $L^{p}$ setting. In particular, we construct critical Hardy weights for the discrete Dirichl…

math.PR2026

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…

math.FA2026

Smoothing on $L^{1}$ for ground state transformed semigroups in non-local settings

Miłosz Baraniewicz, Kamil Kaleta

We study the $L^{1}$ -smoothing properties for a broad class of semigroups arising from the ground state transformation of Schrödinger semigroups with confining potentials associated…

math.PR2025

Heat kernels, intrinsic contractivity and ergodicity of discrete-time Markov chains killed by potentials

Wojciech Cygan, Kamil Kaleta, René L. Schilling +1

We study discrete-time Markov chains on countably infinite state spaces, which are perturbed by rather general confining (i.e.\ growing at infinity) potentials. Using a discrete-ti…

math.SP2025

Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators

Kamil Kaleta, René L. Schilling, Paweł Sztonyk

We study the spatial decay behaviour of resolvent kernels for a large class of non-local Lévy operators and bound states of the corresponding Schrödinger operators. Our findings na…

math.PR2025

Heat kernels and Green functions for fractional Schrödinger operators with confining potentials

Xin Chen, Kamil Kaleta, Jian Wang

We give two-sided, global (in all variables) estimates of the heat kernel and the Green function of the fractional Schrödinger operator with a non-negative and locally bounded pote…

math.FA2023★ 5 cited

Quasi-ergodicity of compact strong Feller semigroups on $L^{2}$

Kamil Kaleta, René L. Schilling

We study the quasi-ergodicity of compact strong Feller semigroups $U_{t}$ , $t > 0$ , on $L^{2} (M, μ)$ ; we assume that $M$ is a locally compact Polish space equipped with a locally finite…

math.SP2023

Density of states for the Anderson model on nested fractals

Hubert Balsam, Kamil Kaleta, Mariusz Olszewski +1

We prove the existence and establish the Lifschitz singularity of the integrated density of states for certain random Hamiltonians $H^{ω} = H_{0} + V^{ω}$ on fractal spaces of infinite diame…

math.FA2023

Integral kernels of Schrödinger semigroups with nonnegative locally bounded potentials

Miłosz Baraniewicz, Kamil Kaleta

We give the upper and the lower estimates of heat kernels for Schrödinger operators $H = - Δ + V$ , with nonnegative and locally bounded potentials $V$ in $R^{d}$ , $d \geq 1$ . We…

math.AP2022

Relativistic stable operators with critical potentials

Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski

We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.

math.FA2022★ 3 cited

Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials

Tomasz Jakubowski, Kamil Kaleta, Karol Szczypkowski

We consider non-local Schrödinger operators $H = - L - V$ in $L^{2} (R^{d})$ , $d \geq 1$ , where the kinetic terms $L$ are pseudo-differential operators which are perturbations of th…

math.PR2022

Exponential densities and compound Poisson measures

Miłosz Baraniewicz, Kamil Kaleta

We prove estimates at infinity of convolutions $f^{n ⋆}$ and densities of the corresponding compound Poisson measures for a class of radial decreasing densities on $\mathbb{R}^d…

math.AP2022

Heat kernels of non-local Schrödinger operators with Kato potentials

Tomasz Grzywny, Kamil Kaleta, Paweł Sztonyk

We study heat kernels of Schrödinger operators whose kinetic terms are non-local operators built for sufficiently regular symmetric Lévy measures with radial decreasing profiles an…

math.PR2021

Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials

Wojciech Cygan, Kamil Kaleta, Mateusz Śliwiński

We propose and study a certain discrete time counterpart of the classical Feynman--Kac semigroup with a confining potential in countable infinite spaces. For a class of long range…

math.PR2021

On directional convolution equivalent densities

Kamil Kaleta, Daniel Ponikowski

We propose a definition of directional multivariate subexponential and convolution equivalent densities and find a useful characterization of these notions for a class of integrabl…

math.PR2019

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 $ℓ$ for random Schrödinger operators $Φ (- Δ) + V^{ω}$ in $L^{2} (R^{d})$ , $d \geq 1$ , where $Φ$ is a co…

math.PR2019

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 $(- Δ)^{α /2} + V^{ω}$ in $L^{2} (R^{d})$ for the full range of $…

math.PR2019

Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators

Kamil Kaleta, René L. Schilling

We study the long-time asymptotic behaviour of semigroups generated by non-local Schrödinger operators of the form $H = - L + V$ ; the free operator $L$ is the generator of a symmetric…

math.PR2018★ 1 cited

Typical long time behaviour of ground state-transformed jump processes

Kamil Kaleta, József Lőrinczi

We consider a class of Lévy-type processes derived via a Doob-transform from Lévy processes conditioned by a control function called potential. These processes have position-depend…

math.PR2018★ 4 cited

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…

math.AP2017

Spatial asymptotics at infinity for heat kernels of integro-differential operators

Kamil Kaleta, Paweł Sztonyk

We study a spatial asymptotic behaviour at infinity of kernels $p_{t} (x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient c…

math.PR2016

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 $t$ , $E_{x} [e^{- \int_{0}^{t} V^{ω} (X_{s}) d s}],$ of a symmetric Lévy process with jumps…

math.PR2015

Contractivity and ground state domination properties for non-local Schrödinger operators

Kamil Kaleta, Mateusz Kwaśnicki, József Lőrinczi

We study supercontractivity and hypercontractivity of Markov semigroups obtained via ground state transformation of non-local Schrödinger operators based on generators of symmetric…

math.SP2015★ 3 cited

Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval

Kamil Kaleta, Mateusz Kwaśnicki, Jacek Małecki

We prove a two-term Weyl-type asymptotic law, with error term O(1/n), for the eigenvalues of the operator psi(-Delta) in an interval, with zero exterior condition, for complete Ber…

Critical discrete Hardy inequalities in Lp

IDS for subordinate Brownian motions in Poisson random environment on nested fractals

Smoothing on L1 for ground state transformed semigroups in non-local settings

Heat kernels, intrinsic contractivity and ergodicity of discrete-time Markov chains killed by potentials

Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators

Heat kernels and Green functions for fractional Schrödinger operators with confining potentials

Quasi-ergodicity of compact strong Feller semigroups on L2

Density of states for the Anderson model on nested fractals

Integral kernels of Schrödinger semigroups with nonnegative locally bounded potentials

Relativistic stable operators with critical potentials

Bound states and heat kernels for fractional-type Schrödinger operators with singular potentials

Exponential densities and compound Poisson measures

Heat kernels of non-local Schrödinger operators with Kato potentials

Decay of harmonic functions for discrete time Feynman--Kac operators with confining potentials

On directional convolution equivalent densities

Lifshitz tail for continuous Anderson models driven by Lévy operators

Lifschitz tail for alloy-type models driven by the fractional Laplacian

Progressive intrinsic ultracontractivity and heat kernel estimates for non-local Schrödinger operators

Typical long time behaviour of ground state-transformed jump processes

Reflected Brownian motion on simple nested fractals

Spatial asymptotics at infinity for heat kernels of integro-differential operators

The quenched asymptotics for nonlocal Schrödinger operators with Poissonian potentials

Contractivity and ground state domination properties for non-local Schrödinger operators

Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval

Critical discrete Hardy inequalities in $L^{p}$

Smoothing on $L^{1}$ for ground state transformed semigroups in non-local settings

Quasi-ergodicity of compact strong Feller semigroups on $L^{2}$