bio | website | mat.uc.cl/~jairo.bochi |
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location | Santiago, Chile | |
age | 39 | |
visits | member for | 5 years, 1 month |
seen | Dec 7 at 16:43 | |
stats | profile views | 215 |
Jul 2 |
awarded | Curious |
Jun 17 |
comment |
Convex hull of total orders
Given a total order $t$ we can associate a permutation $P_t$ matrix in an obvious way. There is a theorem by Birkhoff and von Neumann which says that the convex hull of permutation matrices is the set of doubly stochastic matrices. My first idea would be to relate your question with this theorem. However, it's not clear how to do that. Question: Is there a linear map $L$ such that if a vector $(v_{ij})$ comes (by the rule above) from a total order $t$ then its image $L((v_{ij}))$ is the permutation matrix $P_t$? I don't know. |
May 10 |
awarded | Yearling |
May 6 |
accepted | Distribution of entries of a doubly-sorted random matrix |
May 6 |
comment |
Distribution of entries of a doubly-sorted random matrix
@ofer-zeitouni, I believe you are right about convergence to uniform. Could you post this as an Answer so I can mark the question as answered? |
May 6 |
comment |
Distribution of entries of a doubly-sorted random matrix
Hi @oferzeitouni. "2*400/2^{20} is less than 1/1000". That's ok: You estimated the probability of having a column/row with many ones, while I computed the probability of having a column/row with either many ones or many zeros. |
May 5 |
awarded | Commentator |
May 5 |
comment |
Distribution of entries of a doubly-sorted random matrix
BTW, the probability of having a row or column with at most one entry different form the others is aprox. 1/600, which is indeed quite rare but not extremely rare... |
May 5 |
comment |
Distribution of entries of a doubly-sorted random matrix
I generated the matrix using Numbers spreadsheet; maybe their random number generator is not very good. Apart from this "miracle", the row-sums (8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 19) and the column-sums (6, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14) doesn't seem to be too exceptional. And since the exceptional row with many 1's simply goes to the bottom, it doesn't influence too heavily the result of the experiment. |
May 4 |
revised |
Generalizing a result of Paul Andi Nagy
Replaced $<,>$ by $\langle,\rangle$. |
May 4 |
suggested | approved edit on Generalizing a result of Paul Andi Nagy |
May 4 |
revised |
Distribution of entries of a doubly-sorted random matrix
added 1 character in body |
May 3 |
revised |
Distribution of entries of a doubly-sorted random matrix
added 135 characters in body |
May 3 |
revised |
Distribution of entries of a doubly-sorted random matrix
added 1371 characters in body |
May 3 |
revised |
Distribution of entries of a doubly-sorted random matrix
edited title |
May 3 |
asked | Distribution of entries of a doubly-sorted random matrix |
Dec 26 |
comment |
Getting unique ergodicity from minimality
David, could you provide some references? I'm not familiar with these concepts. BTW, I'm writing a paper where I'll probably need to mention the existence of such examples. |
Dec 21 |
comment |
Getting unique ergodicity from minimality
Amazing! Thank you! |
Dec 21 |
accepted | Getting unique ergodicity from minimality |
Dec 21 |
awarded | Yearling |