论文标题
布朗运动可以感觉到鼓的形状
Brownian motion can feel the shape of a drum
论文作者
论文摘要
我们研究了$ D $维圆环的风景重建问题，证明Matzinger和Lember（2006）获得的傅立叶系数标准也适用于连续的空间。特别是，有了正确的漂移，可以使用布朗运动来重建任何风景。为此，我们证明了无限Vandermonde矩阵的注射属性。
We study the scenery reconstruction problem on the $d$-dimensional torus, proving that a criterion on Fourier coefficients obtained by Matzinger and Lember (2006) for discrete cycles applies also in continuous spaces. In particular, with the right drift, Brownian motion can be used to reconstruct any scenery. To this end, we prove an injectivity property of an infinite Vandermonde matrix.
