科研之友
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摘要
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with the Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial differential, diffusion-like equations. These equations are valid for matrices of arbitrary size and for any initial condition assigned to the process. The solutions have compact integral representation that allows for a simple study of their asymptotic behavior, uncovering the Airy and Pearcey functions.
- 出版日期2015-9
- 单位中国地震局
