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Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in \(\mathbb Z^d\). (English) Zbl 1011.82012
Journées “Équations aux dérivées partielles”, Saint-Jean-de-Monts, France, 31 mai au 4 juin 1999. Exposés Nos. I–XIX. Nantes: Université de Nantes. Exp. No. XVIII, 16 p. (1999).
The author briefly reviews his extensive work on random walks in random potentials in \(d\) dimensions [Ann. Henri Poincaré 2, No. 2, 237–307 (2001; Zbl 1019.81052)]. Using a supersymmetric Gaussian representation the problem is connected to Witten Laplacians.
For the entire collection see [Zbl 0990.00047].
MSC:
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
35R60 PDEs with randomness, stochastic partial differential equations
81T60 Supersymmetric field theories in quantum mechanics
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