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Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1985
A Gaussian measure \(\mu\) on the vector space M(d) of real \(d\times d\) matrices is called isotropic if it is invariant under all automorphisms \(\tau_ u: M(d)\to M(d)\), \(A\mapsto U^{-1}AU\), where \(U\in O(d)\), the group of orthogonal matrices. \(\mu\) is characterized by its covariance C. Let W(t) be an M(d) valued (''additive'') Brownian motion
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A Gaussian measure \(\mu\) on the vector space M(d) of real \(d\times d\) matrices is called isotropic if it is invariant under all automorphisms \(\tau_ u: M(d)\to M(d)\), \(A\mapsto U^{-1}AU\), where \(U\in O(d)\), the group of orthogonal matrices. \(\mu\) is characterized by its covariance C. Let W(t) be an M(d) valued (''additive'') Brownian motion
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American Journal of Physics, 1962
In this paper, we derive the general law for the Brownian motion displacement of a particle in a colloidal solution on the basis of a wave equation for energy, which adequately explains its vibratory character.
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In this paper, we derive the general law for the Brownian motion displacement of a particle in a colloidal solution on the basis of a wave equation for energy, which adequately explains its vibratory character.
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Journal of Statistical Physics, 1986
The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due
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The question of the existence and correct form of equations describing Brownian motion on a manifold cannot be answered by mathematics alone, but requires a study of the underlying physics. As in classical mechanics, manifolds enter through the transformation of variables needed to account for the presence of constraints. The constraints are either due
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A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, 2006
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