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Explore the mathematical theory of zero-range processes and condensation phenomena in this 48-minute conference talk. Delve into interacting particle systems where particles jump between sites at rates determined by occupation numbers and transition probabilities. Learn about the conditions under which condensation occurs when the total number of particles tends to infinity, particularly when the jump rate function is decreasing and the site set is finite. Discover how the majority of particles accumulate at a single site to form a condensate, and understand the Markovian evolution of the condensate's position in appropriate scaling limits. Examine the general framework developed for investigating when state identification in Markov processes preserves Markovian behavior in quotient processes. Follow the main ideas behind the mathematical approach to these problems and explore open questions that remain in this active area of research. The presentation covers applications to various related models and provides insights into the broader field of interacting particle systems and their scaling limits.
