Large deviations for subcomplex counts and Betti numbers in multiparameter simplicial complexes

We consider the multiparameter random simplicial complex as a higher dimensional extension of classical Erdős–Rényi graph. investigate appearance “unusual” topological structures in from point view large deviations. first study upper tail deviation probabilities for subcomplex counts, deriving order magnitude such at logarithmic scale precision. The obtained results are then applied to analyze deviations number simplices complexes. Finally, these also used deduce estimates Betti numbers critical dimension.