Abstract
We show that for any lattice L ⊆ Rn and vectors x, y ∈ Rn, ρ(L + x)2ρ(L + y)2≤ρ(L)2ρ(L+x+y)ρ(L+x-y), where ρ is the Gaussian mass function ρ(A) := ∑w∈A exp(-π||w||2). We show a number of applications, including bounds on the moments of the discrete Gaussian distribution, various monotonicity properties of the heat kernel on at tori, and a positive correlation inequality for Gaussian measures on lattices.
Original language | English (US) |
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Pages (from-to) | 749-757 |
Number of pages | 9 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 31 |
Issue number | 2 |
DOIs | |
State | Published - 2017 |
Keywords
- Gaussian measure
- Heat kernel
- Lattices
- Theta function
ASJC Scopus subject areas
- General Mathematics