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Large Deviation Principle of Multidimensional Multiple Averages on $\mathbb{N}^d$
Jung-Chao Ban, Wen-Guei Hu, Guan-Yu Lai · 2021-06-18 · via math.PR updates on arXiv.org

This paper establishs 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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