# A STUDY ON CONDENSATION IN ZERO RANGE PROCESSES

• Accepted : 2018.09.17
• Published : 2018.09.25

#### Abstract

We investigate the condensation transition of a zero range process with jump rate g given by $g(k)=\left\{\frac{M}{k^{\alpha}},\;if\;k{\leq}an\\{\frac{1}{k^{\alpha}}},\;if\;k>an,$ (0.1), where ${\alpha}$ > 0 and a(0 < a < 1/2) is a rational number. We show that for any ${\epsilon}$ > 0, there exists $M^*$ > 0 such that, for any 0<$M{\leq}M^*$, the maximum cluster size is between ($a-{\epsilon}$)n and ($a+{\epsilon}$)n for large n.

#### Acknowledgement

Supported by : Catholic University of Korea

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