most recent 30 from http://mathoverflow.net 2013-05-19T03:51:09Z http://mathoverflow.net/feeds/user/24899 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/101309/tetris-like-falling-sticky-disks/101317#101317 Nechaev 2012-07-04T16:18:46Z 2012-07-04T16:18:46Z

<p>The density of a randomly growing heap is known, but it is model-dependent and non-universal. The linear dependence of the height on number of deposited blocks is evident, however the coefficient in front of this dependence is again model-dependent. The growth can be viewed as a special sequential matrix multiplication as described in <a href="http://arxiv.org/abs/1110.3524/" rel="nofollow">http://arxiv.org/abs/1110.3524/</a> leading to dynamics of 1D Toda chain. One can play with different versions of this model, for example, supposing that there is only left-hand interaction. The corresponding profile will look different, however the fluctuations will be again of KPZ-type. </p>