**Title:** Diffusive estimates for a tagged particle in zero-range particle

**Speaker:** Professor Sunder Sethuraman

**Speaker Info:** Iow State University

**Brief Description:**

**Special Note**:

**Abstract:**

We consider the motion of a distinguished, or tagged particle interacting with others in a zero-range system. The zero-range particle system is a collection of dependent random walks on the d-dimensional Euclidean lattice where the interaction is in the "time domain." That is, if there are k particles at a vertex, then with rate depending on the number of particles, say g(k), one of the particles jumps to a location according to a transition probability p independent of the other particles.Under some conditions on g and p, we show the tagged particle in equilibrium is diffusive in dimensions d=1 and d>2. We also show, in a case in dimension d=1, an invariance principle for the tagged position.

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