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Annealed Lyapounov exponents and large deviations in a Poissonian potential. II. (English) Zbl 0826.60019
Author’s abstract: We derive a large deviations principle for the position at large time \(t\) of \(d\)-dimensional annealed Brownian motion in a Poissonian potential in critical scale \(t^{d/(d + 2)}\). The rate function is one of the Lyapunov norms constructed in part I (see above). Our large deviation results have a natural application to the study of Brownian motion with a constant drift in a Poissonian potential. They enable to study the transition which occurs between the “small drift” and “large drift” regime.

MSC:
60F10 Large deviations
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References:
[1] J. D. DEUSCHEL and D. W. STROOCK , Large deviations (Academic Press, Boston 1989 ). MR 90h:60026 | Zbl 0705.60029 · Zbl 0705.60029
[2] M. D. DONSKER and S. R. S. VARADHAN , Asymptotics for the Wiener sausage (Comm. Pure Appl. Math., Vol. 28, 1975 , pp. 525-565). MR 53 #1757a | Zbl 0333.60077 · Zbl 0333.60077 · doi:10.1002/cpa.3160280406
[3] T. EISELE and R. LANG , Asymptotics for the Wiener sausage with drift (Prob. Th. Rel. Fields, Vol. 74, 1, 1987 , pp. 125-140). MR 88e:60046 | Zbl 0586.60076 · Zbl 0586.60076 · doi:10.1007/BF01845643
[4] R. S. ELLIS , Entropy, large deviations, and statistical mechanics (Springer, New York, 1985 ). Zbl 0566.60097 · Zbl 0566.60097
[5] P. GRASSBERGER and I. PROCACCIA , Diffusion and drift in a medium with randomly distributed traps (Phys. Rev., Vol. A26, 1982 , pp. 3686-3688).
[6] A. S. SZNITMAN , On long excursions of Brownian motion among Poissonian obstacles , in Stochastic Analysis, M. Barlow and N. Bingham, eds. (London Math. Soc., Lecture Note Series, Cambridge University Press, 1991 , pp. 353-375). MR 93e:60167 | Zbl 0760.60027 · Zbl 0760.60027
[7] A. S. SZNITMAN , Brownian survival among Gibbsian traps (Ann. Probab., Vol. 21, 1, 1993 , pp. 490-508). Article | MR 94d:60157 | Zbl 0769.60104 · Zbl 0769.60104 · doi:10.1214/aop/1176989413 · minidml.mathdoc.fr
[8] A. S. SZNITMAN , Brownian asymptotics in a Poissonian environment (Probab. Th. Rel. Fields, Vol. 95, 1993 , pp. 155-174). MR 94c:60173 | Zbl 0792.60100 · Zbl 0792.60100 · doi:10.1007/BF01192268
[9] A. S. SZNITMAN , Brownian motion with a drift in a Poissonian potential (Comm. Pure Appl. Math., Vol. 47, 10, 1994 , pp. 1283-1318). MR 95m:60122 | Zbl 0814.60021 · Zbl 0814.60021 · doi:10.1002/cpa.3160471002
[10] A. S. SZNITMAN , Shape Theorem, Lyapounov exponents, and large deviations for Brownian motion in a Poissonian potential (Comm. Pure Appl. Math., Vol. 47, 12, 1994 , pp. 1655-1688). MR 96b:60217 | Zbl 0814.60022 · Zbl 0814.60022 · doi:10.1002/cpa.3160471205
[11] A. S. SZNITMAN , Annealed Lyapounov exponents and large deviations in a Poissonian potential I (Ann. Scient. Éc. Norm. Sup. 4e Série, t. 28, 1995 , pp. 345-370). Numdam | MR 97a:60109 | Zbl 0826.60018 · Zbl 0826.60018 · numdam:ASENS_1995_4_28_3_345_0 · eudml:82386
[12] A. S. SZNITMAN , Brownian motion and obstacles, First European Congress of Mathematics , Ed. A. Joseph, F. Mignot, F. Murat, B. Prum and R. Rentschler, 1994 , pp. 225-248, Birkhäuser, Basel (preprint). MR 96d:60125 | Zbl 0815.60077 · Zbl 0815.60077
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