2013 Fiscal Year Final Research Report

Random sequential packing of cubes into torus

Research Project

Project/Area Number	23540177
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Research Field	General mathematics (including Probability theory/Statistical mathematics)
Research Institution	The Institute of Statistical Mathematics
Principal Investigator	ITOH Yoshiaki 統計数理研究所, 大学共同利用機関等の部局等, 名誉教授 (60000212)
Project Period (FY)	2011 – 2013
Keywords	確率論
Research Abstract	Very simplified models are introduced to understand the random sequential packing models mathematically. The 1-dimensional model is sometimes called the Parking Problem. To obtain a 1-dimensional packing density, distribution of the minimum of gaps, etc., the classical analysis has to be studied. The packing density of the general multi-dimensional random sequential packing of cubes (hypercubes) makes a well-known unsolved problem. The experimental analysis is usually applied to the problem. We introduced simplified multi-dimensional models of cubes and torus, which keep the character of the original general model, and introduced a combinatorial analysis for combinatorial modelings. Here we succeeded in obtaining expected number of cube for a corner preference random sequential packing of cubes into a larger cube mathmeatically without using computer simulations, which will help to solve our original problem random sequential packing of cubes into torus.