The study identifies the Poisson boundary of random walks on the mapping class group, suggesting implications for geodesic laminations.
We define an electrification of the curve graph of a surface S of finite type and use it to identify the Poisson boundary of a random walk on the mapping class group of S with some logarithmic moment condition as a stationary measure on the space of minimal and maximal geodesic laminations on S, equipped with the Hausdorff topology.
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Ursula Hamenstädt (2025) studied this question.
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