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We show how correlated steps introduces significant contributions to the modification of the halo mass function in modified gravity models, taking the chameleon models as an example, in the framework of the excursion set approach. This correction applies to both the Lagrangian and Eulerian environments discussed in previous studies. Correlated steps also enhances the modifications arising from the fifth force in the conditional mass function as well as the halo bias. We found that abundance and clustering measurements from different environments can provide strong constraints on the chameleon models.

Excursion set theory for modified gravity: correlated steps, mass functions and halo bias