Let $$Z^1$$ Z 1 and $$Z^2$$ Z 2 be partition functions in the random polymer model in the same environment but driven by different underlying random walks. We give a comparison in concave stochastic order between $$Z^1$$ Z 1 and $$Z^2$$ Z 2 if one of the random walks has “more randomness” than the other. We also treat some related models: The parabolic Anderson model with space–time Lévy noise; Brownian motion among space–time obstacles; and branching random walks in space–time random environments. We also obtain a necessary and sufficient criterion for $$Z^1\preceq _{cv}Z^2$$ Z 1 ⪯ cv Z 2 if the lattice is replaced by a regular tree.

中文翻译：

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时空随机环境下的分区函数比较

设 $$Z^1$$ Z 1 和 $$Z^2$$ Z 2 是相同环境下随机聚合物模型中的分配函数，但由不同的潜在随机游走驱动。如果随机游走中的一个比另一个具有“更多的随机性”，我们将在 $$Z^1$$ Z 1 和 $$Z^2$$ Z 2 之间以凹随机顺序进行比较。我们还处理了一些相关模型：具有时空 Lévy 噪声的抛物线安德森模型；时空障碍间的布朗运动；并在时空随机环境中分支随机游走。如果格子被正则树代替，我们还获得了 $$Z^1\preceq _{cv}Z^2$$Z 1 ⪯ cv Z 2 的充分必要条件。