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<p>In this work, we firstly answer to a question raised by Khoshnevisan (Trans Am Math Soc 359:3125–3151, 2007) [Open Problem 4] by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank is not matching the aforementioned condition, the projection of the zero set is the entirety of the projective space.</p>

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Zeros of the Brownian Sheet

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月6日

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  • Keming Chen,
  • Guillaume Woessner

摘要

In this work, we firstly answer to a question raised by Khoshnevisan (Trans Am Math Soc 359:3125–3151, 2007) [Open Problem 4] by proving that almost surely there is no projection of big enough rank changing the Hausdorff dimension of the zeros of the Brownian sheet. Secondly, we prove that almost surely for every projection whose rank is not matching the aforementioned condition, the projection of the zero set is the entirety of the projective space.