This paper establishes a functional law of large numbers and central limit theorem for marked Hawkes point measures their corresponding shot noise processes. We prove that the normalized random measure can be approximated in distribution by sum Gaussian white process plus an appropriate lifting map correlated one-dimensional Brownian motion. The motion results from self-exciting arrivals events...

We compute the planar limit, as all-order power series in 't Hooft coupling, of various integrated 4-point functions chiral primary operators ${\cal N}=4$ SU(N) super Yang-Mills, and moment map N}=2$ SQCD. do so by computing free energy on $S^4$ respective massive deformations these theories, then taking advantage exact relation between energies functions.

Abstract We consider the problem of counting lattice points contained in domains $$\mathbb {R}^d$$ R d defined by products linear forms. For $$d \ge 9$$ ≥ 9 we show that normalized discrepancies these problems sat...