Large deviation principle of multidimensional multiple averages on Nd

Abstract

This paper establishes the large deviation principle (LDP) for multiple averages on Nd . We extend the previous work of Carinci et al. (2012) to multidimensional lattice Nd for d≥≥2. The same technique is also applicable to the weighted multiple average launched by Fan (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.