BE-condensation from mathematical point of view, and statistical mechanics of the Euler's partitio numerorum

It is well-known that statistics of the partitions of natural numbers (Young diagrams) is the same as the energy statistics of quantum ideal gas models. The new thing which had been appeared recently is the progress in the theory of limit shapes (limit distribution) under the consistent growth of the energy and number of particles (number of summands). This analysis allows us to give pure mathematical exact interpretation of Bose-Einstein condensation in dimensions $d>2$ including fractional dimensions. Our explanation perhaps is not completely new (see, for example, papers by V. Maslov and others), but in any case it points to the importance of new analysis of the limit shapes. This is especially interesting because of the theory of three dimensional Young diagrams and related new study of BE-condensation.