Dan Cheng

activity

20152019

most citedOn the Explicit Height Distribution and Expected Number of Local Maxima of Isotropic Gaussian Random Fields

16 citations · 17 across the 4 of their papers we have counts for

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Showing math.PRShow all

5 papers · 1 filter

math.PR2019

On critical points of Gaussian random fields under diffeomorphic transformations

Dan Cheng, Armin Schwartzman

Let ${X (t), t \in M}$ and ${Z (t^{'}), t^{'} \in M^{'}}$ be smooth Gaussian random fields parameterized on Riemannian manifolds $M$ and $M^{'}$ , respectively, such that $X (t) = Z (f (t))$ , wher…

math.PR2018

Extremes of Spherical Fractional Brownian Motion

Dan Cheng, Peng Liu

Let ${B_{β} (x), x \in S^{N}}$ be a fractional Brownian motion on the $N$ -dimensional unit sphere $S^{N}$ with Hurst index $β$ . We study the excursion probability $\ma…

math.PR2015★ 1 cited

Excursion Probabilities of Isotropic and Locally Isotropic Gaussian Random Fields on Manifolds

Dan Cheng

Let $X = {X (p), p \in M}$ be a centered Gaussian random field, where $M$ is a smooth Riemannian manifold. For a suitable compact subset $D \subset M$ , we obtain the approximations t…

math.PR2015★ 16 cited

On the Explicit Height Distribution and Expected Number of Local Maxima of Isotropic Gaussian Random Fields

Dan Cheng, Armin Schwartzman

The explicit formulae for the height distribution and expected number of local maxima have been obtained for isotropic Gaussian random fields on certain low-dimensional Euclidean s…

math.PR2015

Excursion Probability of Certain Non-centered Smooth Gaussian Random Fields

Dan Cheng

Let $X = {X (t) : t \in T}$ be a non-centered, unit-variance, smooth Gaussian random field indexed on some parameter space $T$ , and let $A_{u} (X, T) = {t \in T : X (t) \geq u}$ be the e…