δ-once-reinforced random walk (ORRW) X_n for some δ>0 is a kind of special reinforced random walk (RRW). In this talk, we show large deviation principle (LDP) for the empirical measure of ORRW on finite tree by the weak convergence approach. In addition, we observe a phase transition of rate function at critical point δ_c=1,i.e. the rate function is less than that of simple random walk (SRW) for δ>1，while they are equal to each other for δ≤1.

This is a joint work with Xiangyu Huang and Kainan Xiang.

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