We study random walks on the Cremona group. We show that almost surely the dynamical degree of a sequence of random Cremona transformations grows exponentially fast, and a random walk produces infinitely many different normal subgroups with probability 1. Moreover, we study the structure of such random subgroups.

中文翻译：

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随机游走、WPD 动作和 Cremona 组

我们研究了克雷莫纳组的随机游走。我们表明，几乎可以肯定，随机 Cremona 变换序列的动态程度呈指数级快速增长，并且随机游走以概率 1 产生无限多个不同的正常子群。此外，我们研究了此类随机子群的结构。