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\\ ==== Next talks ====
[[en:seminaires:SeminaireMod:index|Seminar of Probability and Modeling]]\\
Wednesday June 4, 2025, 2:15PM, Sophie Germain 1013\\
**Joe Jackson** (University of Chicago) //Quantitative convergence for displacement monotone mean field games of control//
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Mean field games of controls (MFGC) are mean field games in which players interact with each other through their controls, in addition to their states. MFGC provide a natural modelling framework in economics, where players (households, firms, etc.) often interact with each other through some macroeconomic variable (price, interest rate, etc.) which is determined by the distribution of the players' controls (consumption vs. saving, production rate, etc.). Mathematically, the main novelty is the appearance of a fixed point equation on the space of measures, which is coupled with the usual equations of MFG theory. In this talk, I will discuss an ongoing joint work with Alpár Mészáros, in which we study the convergence problem for MFGC, i.e. the problem of rigorously justifying the connection between MFGC and the corresponding sequence of finite player games. Our main results provide convergence rates for the equilibria of the finite player games towards their MFGC limit as the number of players goes to infinity. Rather than analyzing the master equation (which seems to be quite challenging in the setting of MFGC), we first prove a convergence result for open-loop equilibria via "forward-backward propagation of chaos", and then transfer this estimate to closed-loop equilibria by using some uniform in N estimates on the N-player Nash system.
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[[en:seminaires:SeminaireMod:index|Seminar of Probability and Modeling]]\\
Wednesday June 25, 2025, 2:15PM, Sophie Germain 1013\\
**Serguei Popov** (CMUP Porto) //Semi-infinite particle systems with exclusion interaction.//
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Abstract: We study semi-infinite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which suppresses jumps that would lead to more than one particle occupying any site. We review some results we have in collaboration with Mikhail Menshikov and Andrew Wade; these are mainly about the behaviour of the leftmost particle (namely, its transience/recurrence properties), and the rate of escape to infinity (in the transient
case). Also we study this process in a random environment, i.e., when these parameters are chosen at random with some common distribution for all the particles, independently; then, we obtain results about the stable cloud decomposition of the system.
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\\ ==== Previous talks ====
\\ === Year 2025 ===

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\\ === Year 2024 ===

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\\ === Year 2023 ===

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\\ === Year 2022 ===

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