Titlebook: Brownian Motion, Obstacles and Random Media; Alain-Sol Sznitman Book 1998 Springer-Verlag Berlin Heidelberg 1998 Brownian bridge.Brownian

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enterprise

Some Potential Theoryollect some results on Green functions. In Section 3 we introduce, à la Chung, equilibrium potentials, equilibrium distributions and capacities by means of last exit distributions. Section 4 develops the maximum principle, the variational principle as well as a number of examples. In Section 5 we li

LEERY

Some Principal Eigenvalue Estimateshrödinger semigroups of Chapter 1 and the bottom of their spectrum. General methods and some first examples are discussed in Section 1. Section 2 presents two instances of the profound link between capacity and bottom of the spectrum. In Section 3 we develop certain one-dimensional bounds on princip

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The Method of Enlargement of Obstaclesn in regions receiving many small and possibly random obstacles. This technique will for instance turn out to be very helpful in the study of various problems related to Poissonian obstacles. The method is outlined in Section 1. The results are then developed in Section 2 (eigenvalue estimates) and

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Offbeat

Quenched Path Measure and Pinning Effectem which also governs the finer asymptotic behavior of the normalizing constant In Section 1 the pinning effect is discussed at a heuristic level. Section 2 shows how a certain weak pinning property can be bootstrapped into a strong pinning property. In Section 3 we introduce a simplified random var

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异端

The Causal and Moral Complexity of Politics, the probabilistic functionals we shall study, and begins the discussion of their functional analytic description. Section 2 introduces the class of potential we shall consider in the sequel. Section 3 studies some properties of the semigroups, which are defined in terms of expectations of Brownian

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