2023/03/20 by Tomoki Inoue, Inoue, Tomoki, Hisayoshi Toyokawa +1
Mathematics · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2303.10873
We show the existence of Lebesgue-equivalent conservative and ergodic σ-finite invariant measures for a wide class of one-dimensional random maps consisting of piecewise convex maps. We also estimate the size of invariant measures around a small neighborhood of a fixed point where the invariant density functions may diverge. Application covers random intermittent maps with critical points or flat points. We also illustrate that the size of invariant measures tends to infinite for random maps whose right branches exhibit a strongly contracting property on average, so that they have a strong recurrence to a fixed point.