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arXiv · 2009.13848

Log-unimodality for free positive multiplicative Brownian motion

Takahiro Hasebe·Yuki Ueda·Jiun-Chau Wang
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Abstract

We prove that the marginal law $\sigma_{t}\boxtimes\nu$ of free positive multiplicative Brownian motion is log-unimodal for all $t>0$ if $\nu$ is a multiplicatively symmetric log-unimodal distribution, and that $\sigma_{t}\boxtimes\nu$ is log-unimodal for sufficiently large $t$ if $\nu$ is supported on a suitably chosen finite interval. Counterexamples are given when $\nu$ is not assumed to be symmetric or having a bounded support.

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Takahiro Hasebe, Yuki Ueda, Jiun-Chau Wang. 2020-09-29. Log-unimodality for free positive multiplicative Brownian motion. https://arxiv.org/abs/2009.13848

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