Abstract
For any positive integer $n$, there exists a unimodal distribution $\mu$ such that $\mu \ast \mu$ is $n$-modal. Furthermore, there is a unimodal distribution $\mu$ such that $\mu \ast \mu$ has infinitely many modes. Lattice analogues of the results are also given.
Citation
Ken-Iti Sato. "Convolution of Unimodal Distributions Can Produce any Number of Modes." Ann. Probab. 21 (3) 1543 - 1549, July, 1993. https://doi.org/10.1214/aop/1176989129
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