In the semi-discrete parabolic Anderson model at high temperature, the partition function admits positive a.s. limits at infinite time and a factorization formula valid up to sub-ballistic scales.
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Uniqueness of global positive time-stationary subexponentially growing solutions to the semidiscrete stochastic heat equation on Z^d (d≥3) with small coupling, via factorization of the point-to-point partition function in the associated polymer model.
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A factorization formula for the partition function in the semi-discrete parabolic Anderson model
In the semi-discrete parabolic Anderson model at high temperature, the partition function admits positive a.s. limits at infinite time and a factorization formula valid up to sub-ballistic scales.
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On global solutions to the semidiscrete stochastic heat equation
Uniqueness of global positive time-stationary subexponentially growing solutions to the semidiscrete stochastic heat equation on Z^d (d≥3) with small coupling, via factorization of the point-to-point partition function in the associated polymer model.