Geodesic
Motivic random variables and representation stability, I: Configuration spaces
Howe, Sean1
1Department of Mathematics, University of Utah, Salt Lake City, UT, United States
Algebraic and Geometric Topology, Tome 20 (2020) no. 6, pp. 3013-3045
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We prove a motivic stabilization result for the cohomology of the local systems on configuration spaces of varieties over ℂ attached to character polynomials. Our approach interprets the stabilization as a probabilistic phenomenon based on the asymptotic independence of certain motivic random variables, and gives explicit universal formulas for the limits in terms of the exponents of a motivic Euler product for the Kapranov zeta function. The result can be thought of as a weak but explicit version of representation stability for the cohomology of ordered configuration spaces. In the sequel, we find similar stability results in spaces of smooth hypersurface sections, providing new examples to be investigated through the lens of representation stability for symmetric, symplectic and orthogonal groups.

Classification : 14G10, 18F30, 55R80
Keywords: representation stability, motivic stabilization, arithmetic statistics, configuration spaces, cohomological stability.

Howe, Sean  1

1 Department of Mathematics, University of Utah, Salt Lake City, UT, United States 
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Howe, Sean. Motivic random variables and representation stability, I: Configuration spaces. Algebraic and Geometric Topology, Tome 20 (2020) no. 6, pp. 3013-3045. http://geodesic.mathdoc.fr/item/AGT_2020_20_6_a7/

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