Reconstructing shredded random matrices

Alex Scott, Oxford
Fine Hall 224

A matrix is given in “shredded” form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matrix is reconstructible if it is uniquely determined by this information. Let M be a random binary n × n matrix, where each entry independently is 1 with probability p = p(n) \le 1/2. Atamanchuk, Devroye and Vicenzo introduced the problem and showed that M is reconstructible with high probability for p > (2 + ε)(log n)/n. Here we find that the sharp threshold for reconstructibility is at (1/2)(log n)/n. Joint work with Paul Balister, Gal Kronenberg and Youri Tamitegama