Brownian motion and parabolic Anderson model in a renormalized Poisson potential

 Access to full text

 Full (PDF)

1. [1] R. Bass, X. Chen and J. Rosen. Large deviations for Riesz potentials of additive processes. Ann. Inst. Henri Poincaré Probab. Stat.45 (2009) 626–666. Zbl1181.60035MR2548497
2. [2] S. Bezerra, S. Tindel and F. Viens. Superdiffusivity for a Brownian polymer in a continuous Gaussian environment. Ann. Probab.36 (2008) 1642–1675. Zbl1149.82032MR2440919
3. [3] M. Biskup and W. König. Screening effect due to heavy lower tails in one-dimensional parabolic Anderson model. J. Statist. Phys.102 (2001) 1253–1270. Zbl1174.82333MR1830447
4. [4] V. S. Borkar. Probability Theory: An Advanced Course. Springer, New York, 1995. Zbl0838.60001MR1367959
5. [5] R. A. Carmona and S. A. Molchanov. Parabolic Anderson Problem and Intermittency. Amer. Math. Soc., Providence, RI, 1994. Zbl0925.35074MR1185878
6. [6] R. A. Carmona and F. G. Viens. Almost-sure exponential behavior of a stochastic Anderson model with continuous space parameter. Stochastics62 (1998) 251–273. Zbl0908.60062MR1615092
7. [7] X. Chen. Random Walk Intersections: Large Deviations and Related Topics. Math. Surv. Mono. 157. Amer. Math. Soc., Providence, RI, 2009. Zbl1192.60002MR2584458
8. [8] X. Chen. Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related Anderson models. Ann. Probab.40 (2012) 1436–1482. Zbl1259.60094MR2978130
9. [9] X. Chen and A. M. Kulik. Asymptotics of negative exponential moments for annealed Brownian motion in a renormalized Poisson potential. Preprint, 2011. Zbl1229.82096MR2812672
10. [10] X. Chen and J. Rosinski. Spatial Brownian motion in renormalized Poisson potential: A critical case. Preprint, 2011. 
11. [11] M. Cranston, D. Gauthier and T. S. Mountford. On large deviations for the parabolic Anderson model. Probab. Theory Related Fields147 (2010) 349–378. Zbl1202.60040MR2594357
12. [12] R. C. Dalang and C. Mueller. Intermittency properties in a hyperbolic Anderson problem. Ann. Inst. Henri Poincaré Probab. Stat.45 (2009) 1150–1164. Zbl1196.60116MR2572169
13. [13] A. de Acosta. Small deviations in the functional central limit theorem with applications to functional laws of the iterated logarithm. Ann. Probab.11 (1983) 78–101. Zbl0504.60033MR682802
14. [14] M. D. Donsker and S. R. S. Varadhan. Asymptotics for the Wiener sausage. Comm. Pure Appl. Math.28 (1975) 525–565. Zbl0333.60077MR397901
15. [15] I. Florescu and F. Viens. Sharp estimation of the almost-sure Lyapunov exponent for the Anderson model in continuous space. Probab. Theory Related Fields135 (2006) 603–644. Zbl1105.60042
16. [16] R. Fukushima. Second order asymptotics for Brownian motion among a heavy tailed Poissonian potential. Preprint, 2010. Zbl1251.60075
17. [17] J. Gärtner, F. den Hollander and G. Maillard. Intermittency on catalysts: Symmetric exclusion. Electron. J. Probab.12 (2007) 516–573. Zbl1129.60061
18. [18] J. Gärtner and W. König. Moment asymptotics for the continuous parabolic Anderson model. Ann. Appl. Probab.10 (2000) 192–217. Zbl1171.60359
19. [19] J. Gärtner, W. König and S. Molchanov. Almost sure asymptotics for the continuous parabolic Anderson model. Probab. Theory Related Fields118 (2000) 547–573. Zbl0972.60056
20. [20] J. Gärtner and S. A. Molchanov. Parabolic problem for the Anderson model. Comm. Math. Phys.132 (1990) 613–655. Zbl0711.60055
21. [21] F. Germinet, P. Hislop and A. Klein. Localization for Schrödinger operators with Poisson random potential. J. Europ. Math. Soc.9 (2007) 577–607. Zbl1214.82053MR2314108
22. [22] S. Harvlin and D. Ben Avraham. Diffusion in disordered media. Adv. in Phys.36 (1987) 695–798. 
23. [23] T. Komorowski. Brownian motion in a Poisson obstacle field. Séminaire Bourbaki 1998/99 (2000) 91–111. Zbl0964.60091MR1772671
24. [24] M. B. Marcus and J. Rosinski. Continuity and boundedness of infinitely divisible process: A Poisson point process approach. J. Theoret. Probab.18 (2005) 109–160. Zbl1071.60025MR2132274
25. [25] L. A. Pastur. The behavior of certain Wiener integrals as $t\to \infty$ and the density of states of Schrödinger equations with random potential. Teoret. Mat. Fiz.32 (1977) 88–95. Zbl0353.60053MR449356
26. [26] A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, Berlin, 1983. Zbl0516.47023MR710486
27. [27] T. Povel. Confinement of Brownian motion among Poissonian obstacles in ${ℝ}^d$, $d\ge 3$. Probab. Theory Related Fields114 (1999) 177–205. Zbl0943.60082MR1701519
28. [28] B. S. Rajput and J. Rosinski. Spectral representations of infinitely divisible processes. Probab. Theory Related Fields82 (1989) 451–487. Zbl0659.60078MR1001524
29. [29] J. Rosinski. On path properties of certain infinitely divisible process. Stochastic Process. Appl.33 (1989) 73–87. Zbl0715.60051MR1027109
30. [30] G. Stolz. Non-monotonic random Schrödinger operators: The Anderson model. J. Math. Anal. Appl.248 (2000) 173–183. Zbl0974.47034MR1772589
31. [31] A.-L. Sznitman. Brownian Motion, Obstacles and Random Media. Springer, Berlin, 1998. Zbl0973.60003MR1717054
32. [32] M. van den Berg, E. Bolthausen and F. den Hollander. Brownian survival among Poissonian traps with random shapes at critical intensity. Probab. Theory Related Fields132 (2005) 163–202. Zbl1072.60067MR2199290