“…An important concept to study quantum noise and correlations in many body fermionic systems is the counting statistics (CS), which characterises the fluctuations of the number of particles N D inside a domain D. Applications include shot noise [1], quantum transport [2,3], quantum dots [4,5], spin and fermionic chains [6][7][8][9], trapped fermions [10,11]. In the related context of random matrix theory (RMT), the statistics of the number of eigenvalues in an interval also generated a lot of interest [6,[12][13][14][15][16][17][18][19][20][21][22][23]. The CS is particularly important for non interacting fermions because of its connection [24][25][26][27] to the bipartite entanglement entropy (EE) of the subsystem D with its complement D. The EE is a highly non local quantity, much studied in the context of quantum information [28], conformal field theory [29][30][31], topological phases [32], quantum phase transitions [33,34], or quantum spin chains [35,36].…”