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Zbl 1041.60079
Mejane, Olivier
Upper bound of a volume exponent for directed polymers in a random environment. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 3, 299-308 (2004). ISSN 0246-0203

Summary: We consider the model of directed polymers in a random environment introduced by Petermann: the random walk is $\Bbb R^d$-valued and has independent $\cal N(0,I_d)$-increments, and the random medium is a stationary centered Gaussian process $(g(k,x), k\geqslant 1, x \in \Bbb R^d)$ with covariance matrix cov$(g(i,x),g(j,y))=\delta_{ij}\Gamma(x-y)$, where $\Gamma$ is a bounded integrable function on $\Bbb R^d$. For this model, we establish an upper bound of the volume exponent in all dimensions $d$.

MSC 2000:: *60K37 Processes in random environments
60G42 Martingales with discrete parameter
82D30 Random media, etc.

Keywords: directed polymers in random environment; Gaussian environment

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