  We study a large class of 1D reaction diffusion models with quenched disorder
using a real space renormalization group method (RSRG) which yields exact
results at large time. Particles (e.g. of several species) undergo diffusion
with random local bias (Sinai model) and react upon meeting. We obtain the
large time decay of the density of each specie, their associated universal
amplitudes, and the spatial distribution of particles. We also derive the
spectrum of exponents which characterize the convergence towards the asymptotic
states. For reactions with several asymptotic states, we analyze the dynamical
phase diagram and obtain the critical exponents at the transitions. We also
study persistence properties for single particles and for patterns. We compute
the decay exponents for the probability of no crossing of a given point by,
respectively, the single particle trajectories ($\theta$) or the thermally
averaged packets ($\bar{\theta}$). The generalized persistence exponents
associated to n crossings are also obtained. Specifying to the process $A+A \to
\emptyset$ or A with probabilities $(r,1-r)$, we compute exactly the exponents
$\delta(r)$ and $\psi(r)$ characterizing the survival up to time t of a domain
without any merging or with mergings respectively, and $\delta_A(r)$ and
$\psi_A(r)$ characterizing the survival up to time t of a particle A without
any coalescence or with coalescences respectively. $\bar{\theta}, \psi, \delta$
obey hypergeometric equations and are numerically surprisingly close to pure
system exponents (though associated to a completely different diffusion
length). Additional disorder in the reaction rates, as well as some open
questions, are also discussed.
