Abstract: 
When we analyze asymptotic behavior of probabilistic cellular automata, we have an assumption called reduction relation which reduce occurrence probability of long length patterns into that of short length patterns. Utilizing the reduction relation and equilibrium equations of the occurrence probability of patterns, we can derive a fundamental diagram which shows relationship between mean flux and density of conserved quantities as asymptotic behavior of probabilistic cellular automata. However, we only confirm existence of the reduction relation with numerical experiments. In the talk, we discuss existence of the reduction relation mathematically and introduce a method for asymptotic analysis without the relation utilizing methods for stochastic processes such as transition probability matrix. 
