## Abstract

The stochastic Anderson model in discrete or continuous space is defined for a class of non-Gaussian spacetime potentials W as solutions u to the multiplicative stochastic heat equation u(t,x)=1+ ∫_{0} ^{t} κΔ u(s,x)ds + ∫_{0}^{t} βW (ds, x) u(s, x) with diffusivity κ and inverse-temperature β. The relation with the corresponding polymer model in a random environment is given. The large time exponential behavior of u is studied via its almost sure Lyapunov exponent λ = lim_{t→∞} t^{-1} log u(t, x), which is proved to exist, and is estimated as a function of β and κ for β^{2} κ^{-1} bounded below: positivity and nontrivial upper bounds are established, generalizing and improving existing results. In discrete space λ is of order β^{2}/log (β^{2}/κ) and in continuous space it is between β^{2} (κ/β^{2}) ^{H/(H+1)} and β^{2} (κ/β^{2}) ^{H/(1+3H)}.

Original language | English |
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Pages (from-to) | 451-473 |

Number of pages | 23 |

Journal | Stochastics and Dynamics |

Volume | 8 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 |

## All Science Journal Classification (ASJC) codes

- Modelling and Simulation