  We consider a graphene sheet in the vicinity of a substrate, which contains
charged impurities. An analytic expression for the probability distribution
function of voltage fluctuations due to the charged impurities is derived. The
distribution function is shown to be non-Gaussian. The voltage fluctuations
lead to the appearance of randomly distributed density inhomogeneities in the
graphene plane. We argue that these disorder-induced density fluctuations
produce a finite conductivity even at a zero gate voltage in accordance with
recent experimental observations. We estimate the width of the minimal
conductivity plateau and the typical size of the electron and hole puddles. The
existence of inhomogeneous random puddles of electrons and holes should be a
generic feature of all graphene layers at low gate voltages due to the
invariable presence of charged impurities in the substrate.
