# Bounding sum of samples of a Gaussian

Suppose we have $K$ points $x_1,\ldots,x_K$ in $\mathbb{R}^d$ and let $$f(x)=\sum_{k=1}^K \exp(-\lambda \Vert x-x_k \rVert^2).$$ Can we uniformly bound $f$ independent of $K$?

It is okay to use some assumption on the distribution of $\{x_k\}$.