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We study fluctuation effects in the two-species reaction-diffusion system  A  +  B  → Ø and  A  +  A  → (Ø,  A ). In contrast to the usually assumed ordinary short-range diffusion spreading of the reactants we consider anomalous diffusion due to microscopic long-range hops. In order to describe the latter, we employ the Lévy stochastic ensemble. The probability distribution for the Lévy flights decays in  d  dimensions with the distance  r  according to a power-law  r  − d − σ  . For anomalous diffusion (including Lévy flights) the critical dimension  d   c   =  σ  depends on the control parameter  σ , 0  &lt;  σ ≤ 2. The model is studied in terms of the field theoretic approach based on the Feynman diagrammatic technique and perturbative renormalization group method. We demonstrate the ideas behind the  B  particle density calculation.

Two-Species Reaction-Diffusion System: the Effect of Long-Range Spreading