Generalized transport inequalities and concentration bounds for Riesz-type gases (Q6614482)

The authors have established several transport and concentration inequalities that serve to explore the connection between a generalized Riesz electric energy and the norms on the set of probability measures defined in terms of duality. These inequalities are a series of Moser-Trudinger like inequalities, which may also be interpreted as bounds on Laplace transform of fluctuations. Among other results, the paper investigates the thermal equilibrium measure for Riesz and more general interaction. The type of interactions treated could be termed as interactions that qualitatively behave like Riesz potentials in both real spaces and Fourier space. The paper provides a rich bibliography and many open problems that could be resolve using the results establish in the paper.