  We study the low temperature conductivity of the electron accumulation layer
induced by the very strong electric field at the surface of $\text{SrTiO}_3$
sample. Due to the strongly nonlinear lattice dielectric response, the
three-dimensional density of electrons $n(x)$ in such a layer decays with the
distance from the surface $x$ very slowly as $n(x) \propto 1/x^{12/7}$. We show
that when the mobility is limited by the surface scattering the contribution of
such a tail to the conductivity diverges at large $x$ because of growing time
electrons need to reach the surface. We explore truncation of this divergence
by the finite sample width, by the bulk scattering rate, or by the crossover to
the bulk linear dielectric response with the dielectric constant $\kappa$. As a
result we arrive at the anomalously large mobility, which depends not only on
the rate of the surface scattering, but also on the physics of truncation.
Similar anomalous behavior is found for the Hall factor, the magnetoresistance,
and the thermopower.

Mesoscale and Nanoscale Physics