Quenched asymptotics for Brownian motion in generalized Gaussian potential. (English) Zbl 1294.60101

The authors summarize the content of this paper in the abstract as follows: We study the long-term asymptotics for the quenched moment consisting of a \(d\)-dimensional Brownian motion and a generalized Gaussian field \(V\). The major progress made in this paper includes: the solution to an open problem posted by R. A. Carmona and S. A. Molchanov [Probab. Theory Relat. Fields 102, No. 4, 433–453 (1995; Zbl 0827.60051)], the quenched laws for Brownian motions in Newtonian-type potentials and in the potentials driven by white noise or by fractional white noise.


60J65 Brownian motion
60K37 Processes in random environments
60K40 Other physical applications of random processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F10 Large deviations


Zbl 0827.60051
Full Text: DOI arXiv Euclid


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