Wüthrich, Mario V. Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential. (English) Zbl 0935.60099 Ann. Probab. 26, No. 3, 1000-1015 (1998). Summary: We consider \(d\)-dimensional Brownian motion in a truncated Poissonian potential conditioned to reach a remote location. If Brownian motion starts at the origin and ends in a hyperplane at distance \(L\) from the origin, the transverse fluctuation of the path is expected to be of order \(L^\xi\). We are interested in a lower bound for \(\xi\). We first show that \(\xi\geq 1/2\) in dimensions \(d\geq 2\) amd then we prove superdiffusive behavior for \(d=2\), resulting in \(\xi\geq 3/5\). Cited in 14 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) Keywords:Brownian motion; Poissonian potential; fluctuation; superdiffusivity PDFBibTeX XMLCite \textit{M. V. Wüthrich}, Ann. Probab. 26, No. 3, 1000--1015 (1998; Zbl 0935.60099) Full Text: DOI References: [1] Huse, D. A. and Henley, C. L. (1985). Pinning and roughening of domain walls in Ising systems due to random impurities. Phys. Rev. Lett. 54 2708-2711. [2] Huse, D. A., Henley, C. L. and Fisher, D. S. (1985). Phys. Rev. Lett. 55 2924-2924. [3] Kardar, M. (1985). Roughening by impurities at finite temperatures. Phys. Rev. Lett. 55 2923-2923. [4] Kardar, M., Parisi, G. and Zhang, Y.-C. (1986). Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56 889-892. · Zbl 1101.82329 [5] Krug, J. and Spohn, H. (1991). Kinetic roughening of growing surfaces. In Solids Far from Equilibrium (C. Godr eche, ed.) 479-582. Cambridge Univ. Press. [6] Licea, C., Newman, C. M. and Piza, M. S. T. (1996). Superdiffusivity in first-passage percolation. Probab. Theory Related Fields 106 559-591. · Zbl 0870.60096 [7] Newman, C. M. and Piza, M. S. T. (1995). Divergence of shape fluctuations in two dimensions. Ann. Probab. 23 977-1005. · Zbl 0835.60087 [8] Sznitman, A.-S. (1994). Shape theorem, Lyapounov exponents and large deviations for Brownian motion in a Poissonian potential. Comm. Pure Appl. Math. 47 1655-1688. · Zbl 0814.60022 [9] Sznitman, A.-S. (1996). Distance fluctuations and Lyapounov exponents. Ann. Probab. 24 1507-1530. · Zbl 0871.60088 [10] W üthrich, M. V. (1998). Fluctuation results for Brownian motion in a Poissonian potential. To appear in Ann. Inst. H. Poincaré Probab. Statist. 34 3. · Zbl 0909.60073 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.