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

  • Johannes Sjöstrand
Part of the Pseudo-Differential Operators book series (PDO, volume 14)


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 Poincaré 7(6):1035–1064, 2006) with some input also from Bordeaux Montrieux (Loi de Weyl presque sûreet résolvante pour des opérateurs différentiels nonautoadjoints, thèse, CMLS, Ecole Polytechnique, 2008) and Hager–Sjöstrand (Math Ann 342(1):177–243, 2008). Some of the general ideas appear perhaps more clearly in this special situation.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Johannes Sjöstrand
    • 1
  1. 1.Université de Bourgogne Franche-ComtéDijonFrance

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