Speaker
Description
We present a new approach to constraining the shape of the CIB source counts below the confusion limit, using the information contained in the tail of the image P(D) distribution. Applying the peaks-over-threshold formalism of extreme-value theory, we model the exceedances with a Generalized Pareto Distribution (GPD), whose shape parameter ξ is formally invariant to the map's mean, gain and count normalization. The method therefore sidesteps much of the instrument-specific modelling that a conventional forward-modelled P(D) fit requires. We show that ξ(u) is a flux-resolved measure of the local logarithmic slope of dN/dS at the intrinsic flux selected by the threshold u, while its modulation under gravitational lensing — the shift Δξ(u) between matched lensed and unlensed fields — tracks the local curvature of the counts, cancels common-mode systematics, and, with an externally known magnification, supplies a calibrated ruler that reaches intrinsic fluxes below the unlensed faint limit. We give simple analytic expressions for these dependences, validate them with realistic simulations including instrument noise, beam smoothing and source blending, and present the current constraints from Planck and Herschel/SPIRE 350 μm data, where the lensing signature is not yet detected and we report upper limits. (Basu, Guerrero & Bertoldi 2026, to be submitted)