# Again on discrete gaussians over lattices [duplicate]

Define $$\rho_{s,c}(x) = exp(-\pi \cdot \frac{\|x - c\|^2}{s^2})$$ and $$\rho_{s,c}(L) = \sum_{x \in L} \rho_{s,c}(x)$$

Then Discrete Gaussian over $$L$$ with center $$c$$ and standard deviation $$s$$ is the following distribution over lattice points: probability of $$v \in L$$ equals:

$$\mathbb{P}[v] = \frac{\rho_{s,c}(v)}{\rho_{s,c}(L)}$$