TY  - INPR
A1  - Klein, Markus
A1  - Léonard, Christian
A1  - Rosenberger, Elke
T1  - Agmon-type estimates for a class of jump processes
N2  - In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 6 
KW  - finsler distance
KW  - decay of eigenfunctions
KW  - jump process
KW  - Dirichlet form
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56995
ER  - 
TY  - JOUR
A1  - Klein, Markus
A1  - Rosenberger, Elke
T1  - Tunneling for a class of difference operators
JF  - ANNALES HENRI POINCARE
N2  - We analyze a general class of difference operators on where is a multi-well potential and is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrodinger operator [see Helffer and Sjostrand in Commun Partial Differ Equ 9:337-408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
Y1  - 2012
U6  - https://doi.org/10.1007/s00023-011-0152-x
SN  - 1424-0637
VL  - 13
IS  - 5
SP  - 1231
EP  - 1269
PB  - Springer
CY  - Basel
ER  - 
TY  - INPR
A1  - Klein, Markus
A1  - Rosenberger, Elke
T1  - Tunneling for a class of difference operators
N2  - We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1 (2012) 5 
KW  - semi-classical difference operator
KW  - tunneling
KW  - interaction matrix
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-56989
ER  -