Integrable interacting particle models: exact solutions and universal scaling limits

Stochastic lattice systems of interacting particles serve as a laboratory for studying the large-scale behaviour of many random phenomena. To some of them in space-time dimensions 1 + 1 the toolbox of the theory of integrable systems can be applied, which makes it possible, at least potentially, to obtain an exact solution of evolution equations that provides a statistical description of particle dynamics. In turn, under a special scaling the exact statistics often converge to universal laws with the range of applicability that extends to whole universality classes unifying many phenomena of different origin far beyond the realm of integrable models. In the talk I will follow the way from particle models to universal laws using examples of integrable systems within the Kardar-Parisi-Zhang universality class and beyond.