Learning models on rooted regular trees with majority update policy: Convergence and phase transition
Moumanti Podder, Anish Sarkar · Advances in Applied Probability · 2026
Abstract We study a model of social learning on rooted regular trees. An agent is stationed at each vertex of double struck upper T Subscript m T m $\mathbb{T}_{m}$ , the rooted tree in which each vertex has precisely m children, and at any time step t element of double struck upper N 0 t ∈ N 0 $t \in \mathbb{N}_{0}$ , the agent is allowed to select one of two available technologies: B and R . Let the technology chosen by the agent at vertex v of double struck upper T Subscript m T m $\mathbb{T}_{m}$ , at time step t , be upper C Subscript t Baseline left parenthesis v right parenthesis C t ( v ) $C_{t}(v)$ . We begin with the independent and identically distributed (i.i.d.) collection StartSet upper C 0 left parenthesis v right parenthesis colon v element of double struck upper T Subscript m Baseline EndSet { C 0 ( v ) : v ∈ T m } $\{C_{0}(v)\,:\, v \in \mathbb{T}_{m}\}$ , where upper C 0 left parenthesis v right parenthesis equals upper B C 0 ( v ) =