  Noise-shaping quantization techniques are widely used for converting
bandlimited signals from the analog to the digital domain. They work by
"shaping" the quantization noise so that it falls close to the reconstruction
operator's null space. We investigate the compatibility of two such schemes,
specifically $\Sigma\Delta$ quantization and distributed noise-shaping
quantization, with random samples of bandlimited functions. Let $f$ be a
real-valued $\pi$-bandlimited function. Suppose $R>1$ is a real number and
assume that $\{x_i\}_{i=1}^m$ is a sequence of i.i.d random variables uniformly
distributed on $[-\tilde{R},\tilde{R}]$, where $\tilde{R}>R$ is appropriately
chosen. We show that by using a noise-shaping quantizer to quantize the values
of $f$ at $\{x_i\}_{i=1}^m$, a function $f^{\sharp}$ can be reconstructed from
these quantized values such that $\|f-f^{\sharp}\|_{L^2[-R, R]}$ decays with
high probability as $m$ and $\tilde{R}$ increase. We emphasize that the sample
points $\{x_i\}_{i=1}^m$ are completely random, i.e., they have no predefined
structure, which makes our findings the first of their kind.
