The PDF perspective on the tracer-matter connection: Lagrangian bias and non-Poissonian shot noise

Understand

We study the connection of matter density and its tracers from the PDF perspective.

• One aspect of this connection is the conditional expectation value $\langle \delta_{\mathrm{tracer}}|\delta_m\rangle$ when averaging both tracer and matter density over some scale.
• We present a new way to incorporate a Lagrangian bias expansion of this expectation value into standard frameworks for modelling the PDF of density fluctuations and counts-in-cells statistics.
• Using N-body simulations and mock galaxy catalogs we confirm the accuracy of this expansion and compare it to the more commonly used Eulerian parametrization.