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In this note we relate the Hamiltonian of the integrable non-compact spin $s$XXZ chain to the Markov generator of a stochastic particle process. The hoppingrates of the continuous-time process are identified with the ones of a q-Hahnasymmetric zero range model. The main difference with the asymmetric simpleexclusion process (ASEP), which can be mapped to the ordinary XXZ spin chain,is that multiple particles can occupy one and the same site. For thenon-compact spin $\frac{1}{2}$ XXZ chain the associated stochastic processreduces to the multiparticle asymmetric diffusion model introduced bySasamoto-Wadati.

The non-compact XXZ spin chain as stochastic particle process