In the 1970s, William Tutte developed a clever algebraic approach, based on certain "invariants", to solve functional equation that arises in enumeration of properly colored triangulations. The plane lattice walks confined first quadrant is governed by similar equations, and has led past 20 years rich collection attractive results dealing with nature (algebraic, D-finite or not) associated gene...

We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the similar path integral formulation without the assumption of mesoscopic systems. It has been clarified that the saddle point method for the path integral is not ...

This lectures deals with photon counting in the framework of biophotonic measurements, that are usually characterized by very low count rates. First, photon counting is introduced from an experimental point of view. Then, the main equations of statistics of photon counts are derived, and their consequences in terms of so-called photon or shot noise are discussed. The moment-analysis is introduc...