We show that for a family of randomly kicked Hamilton–Jacobi equations on the torus, almost surely, the solution of an initial value problem converges exponentially fast to the unique stationary solution. Combined with the earlier results of the authors, this completes the program in the multi-dimensional setting started by E, Khanin, Mazel and Sinai in the one-dimensional case.

中文翻译：

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Hamilton-Jacobi随机方程解的指数收敛性

我们显示出，对于环上的随机踢的Hamilton–Jacobi方程组，几乎可以肯定地，初值问题的解以指数形式快速收敛到唯一的平稳解。结合作者的较早结果，这完成了由E，Khanin，Mazel和Sinai在一维案例中启动的多维环境中的程序。