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2021 NCTS Seminar on Dynamical Systems
 
16:00 - 17:00, November 23, 2021 (Tuesday)
Zoom, Online seminar
(線上演講 Zoom)
Large Deviation Principle of Multidimensional Multiple Averages on $ \ mathbb{N}^d$
Guan-Yu Lai (National Chengchi University)

Abstract:

This paper establishes the large deviation principle (LDP) for multiple averages on $\mathbb{N}^d$. We extend the previous work of [Carinci et al., Indag. Math. 2012] to multidimensional lattice $ \ mathbb{N}^d$ for $d \geq 2$. The same technique is also applicable to the weighted multiple average launched by Fan [Fan, Adv. Math. 2021]. Finally, the boundary conditions are imposed to the multiple sum and explicit formulae of the energy functions with respect to the boundary conditions are obtained.

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