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Exponential mixing for the randomly forced NLS equation
Yuxuan Chen, Shengquan Xiang, Zhifei Zhang, Jia-Cheng Zhao
https://arxiv.org/abs/2506.10318 https:/…

Exponential mixing for the randomly forced NLS equation
This paper investigates exponential mixing of the invariant measure for randomly forced nonlinear Schrödinger equation, with damping and random noise localized in space. Our study emphasizes the crucial role of exponential asymptotic compactness and control properties in establishing the ergodic properties of random dynamical systems. This work extends the series [15, 45] on the statistical behavior of randomly forced dispersive equations.

Abandoned Police Station
Baywatch Nights 2x09 - Night Whispers
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Random Sperner lemma and random Brouwer fixed point theorem
Qiang Tu, Xiaohuan Mu, Tiexin Guo, Goong Chen
https://arxiv.org/abs/2507.08521 https://

Random Sperner lemma and random Brouwer fixed point theorem
In this paper, we systematically develop the theory of $L^{0}$-simplicial subdivisions of $L^{0}$-simplexes by grasping the inherent connection between $L^{0}$-simplexes and usual simplexes. We establish a key representation theorem of a proper $L^0$-labeling function by usual proper labeling functions. Based on the representation theorem, we can establish a general random Sperner lemma. Next, as an application of the random Sperner lemma, we give a complete proof of the known random Brouwer fi…

I think he's calling for help
Season 9 Episode 4 "Dolphin Quest"
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Season 7 Episode 15 "Life Guardian"
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Baywatch Nights 2x19 - The Eighth Seal
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Season 4 Episode 13 "The Red Knights"
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Season 6 Episode 22 "Go For The Gold"
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Season 4 Episode 14 "Coronado Del Soul: part 1"
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Loving Rupert
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Season 4 Episode 14 "Coronado Del Soul: part 1"
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