Some constructions of diffuse invariant random subgroups

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2025

Tezin Dili: İngilizce

Öğrenci: EGEMEN ÇEKEN

Danışman: Burak Kaya

Özet:

Invariant random subgroups (abbreviated IRSs), which are conjugation invariant Borel probability measures on the space of subgroups of a countable group, emerged as a probabilistic generalization of normal subgroups and lattices. An active area of research is finding and classifying IRSs of a given countable group. In order to understand arbitrary IRSs, it is sufficient to understand ergodic IRSs since the ergodic decomposition theorem allows us to write arbitrary IRSs in terms of ergodic IRSs. Among ergodic IRSs, Thomas recently distinguished those that do not assign full measure to an isomorphism class, namely, the diffuse IRSs. So far, there have not been many examples of diffuse IRSs. This thesis is intended to give a survey of two different IRS constructions that satisfy diffuseness and related properties.