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RESEARCH PRODUCT

Weyl Asymptotics and Random Perturbations in a One-Dimensional Semi-classical Case

Johannes Sjöstrand

subject

Pure mathematicsRange (mathematics)symbols.namesakeOperator (computer programming)Simple (abstract algebra)Dimension (graph theory)Poincaré conjecturesymbolsMathematics

description

We consider a simple model operator P in dimension 1 and show how random perturbations give rise to Weyl asymptotics in the interior of the range of P. We follow rather closely the work of Hager (Ann Henri Poincare 7(6):1035–1064, 2006) with some input also from Bordeaux Montrieux (Loi de Weyl presque sureet resolvante pour des operateurs differentiels nonautoadjoints, these, CMLS, Ecole Polytechnique, 2008) and Hager–Sjostrand (Math Ann 342(1):177–243, 2008). Some of the general ideas appear perhaps more clearly in this special situation.

yearjournalcountryeditionlanguage
2019-01-01
https://doi.org/10.1007/978-3-030-10819-9_3