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CATEGORIES:Probability
SUMMARY:Stability of the elliptic Harnack Inequality - Mar
tin Barlow (UBC)
DTSTART;TZID=Europe/London:20220905T163000
DTEND;TZID=Europe/London:20220905T173000
UID:TALK178463AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178463
DESCRIPTION:A manifold has the Liouville property if every bou
nded harmonic function is constant. A theorem of T
.\\ Lyons is that the Liouville property is not pr
eserved under mild perturbations of the space. St
ronger conditions on a space\, which imply the Lio
uville property\,are the parabolic and elliptic Ha
rnack inequalities (PHI and EHI). In the early 199
0s Grigor'yan and Saloff-Coste gave a characterisa
tion of the parabolic Harnack inequality (PHI)\, w
hich immediately gives its stability under mild pe
rturbations. In this talk we prove the stability
of the EHI. The proof uses the concept of a quasi
symmetric transformation of a metric space\, and t
he introduction of these ideas to Markov processes
suggests a number of new problems. (Based on joi
nt work with Mathav Murugan.)
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Jason Miller
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