wiener measures
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2012 ◽  
pp. 1275-1330 ◽  
Author(s):  
Andrea Nahmod ◽  
Tadahiro Oh ◽  
Luc Rey-Bellet ◽  
Gigliola Staffilani




2011 ◽  
Vol 40 (3) ◽  
Author(s):  
Christian Bär ◽  
Frank Pfäffle




2006 ◽  
Vol 137 (3-4) ◽  
pp. 289-321 ◽  
Author(s):  
Tadahisa Funaki ◽  
Kensuke Ishitani


Author(s):  
Andreas Eberle

We study spectral gaps w.r.t. marginals of pinned Wiener measures on spaces of discrete loops (or, more generally, pinned paths) on a compact Riemannian manifold M. The asymptotic behaviour of the spectral gap as the time parameter T of the underlying Brownian bridge goes to 0 is investigated. It turns out that depending on the choice of a Riemannian metric on the base manifold, very different asymptotic behaviours can occur. For example, on discrete loop spaces over sufficiently round ellipsoids the gap grows of order α/T as T ↓ 0. The strictly positive rate α stabilizes as the discretization approaches the continuum limit. On the other extreme, if there exists a closed geodesic γ : S1 → M such that the sectional curvature on γ(S1) is strictly negative, and the loop is pinned close to γ(S1), then the gap decays of order exp (-β/T), and the decay rate β approaches +∞ as the discretization approaches the continuum limit.





1987 ◽  
Vol 28 (1) ◽  
pp. 85-102 ◽  
Author(s):  
Ingrid Daubechies ◽  
John R. Klauder ◽  
Thierry Paul


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