Boltzmann–Grad asymptotic behavior of collisional dynamics Page 1 Reviews in
Mathematical Physics Vol. 33, No. 2 (2021) 2130001 (32 pages) c World Scientific …

We present a quantitative analysis of the Boltzmann–Grad (low-density) limit of a hard
sphere system. We introduce and study a set of functions, the correlation errors, measuring …

We introduce a new approach to justify mean-field limits for first-and second-order particle
systems with singular interactions. It is based on a duality approach combined with the …

The paper develops an approach to the description of the evolution of correlations for many
hard spheres based on a hierarchy of evolution equations for the cumulants of the …

The article deals with the challenge of the construction of solutions to hierarchies of
fundamental evolution equations for many colliding particles. The method of cluster …

The paper deals with a rigorous description of the kinetic evolution of a hard sphere system
in the low‐density (Boltzmann–Grad) scaling limit within the framework of marginal …

The review presents rigorous results of the theory of fundamental equations of evolution of
many-particle systems with collisions and also considers their connection with nonlinear …

In the paper the possible approaches to the rigorous derivation of the Boltzmann kinetic
equation with hard sphere collisions from underlying dynamics are considered. In particular …

We develop a rigorous formalism for the description of the kinetic evolution of many-particle
systems with dissipative interaction. The links of the evolution of a hard sphere system with …

The chapter presents some new approaches to describing the collective behavior of
complex systems of mathematical biology based on the evolution equations of observables …