Buongiorno a tutti, Vorremmo segnalarvi che venerdì prossimo (24 Gennaio) in aula 2AB40 (Torre Archimede, Università di Padova) ci sarà un seminario per il ciclo di seminari in Probabilità e Finanza di: Orphée Collin (LPSM Paris) Title: Two-dimensional simple random walk conditioned on avoiding 0 and two-dimendional random interlacements Date: January 24, 2025, at 14:30, room 2AB40 Abstract: In this talk, I will present joint works with Francis Comets and Serguei Popov. How can one condition the two-dimensional simple random walk (2D-SRW), which is well known to be recurrent, on not hitting the origin ? This question will be answered by defining rigorously the 2D-SRW conditioned to avoid the origin. I will then discuss some of its surprising properties and present results concerning its speed of escape towards infinity. I will also present the random interlacements model build upon the conditioned 2D-SRW, which was introduced by the aforementioned coauthors (together with Marina Vachkovskaia) in 2015. I will discuss some properties of this model : FKG inequality, 0-1 law, phase transition and behavior at criticality. During the talk, I will also evoke the continuous counterparts of these processes, namely : the two-dimensional Brownian motion conditioned to avoid the unit ball and the two-dimensional random interlacements. If time allows, I will mention some results on the Brownian random interlacements. Vi aspettiamo numerosi! Alberto Chiarini e Alekos Cecchin