bio | website | mat.uc.cl/~jairo.bochi |
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location | Santiago, Chile | |
age | 40 | |
visits | member for | 5 years, 9 months |
seen | Jul 31 at 14:46 | |
stats | profile views | 241 |
Jul 14 |
comment |
A metric for Grassmannians
"Natural" metrics on the Grassmannian should be invariant under isometries of the undelying Euclidian space. Actually there are many such metrics, and this nice paper gives a general method for constructing them: Qiu, Zhang, Li, "Unitarily invariant metrics on the grassmann space". SIAM J. Matrix. Anal. Appl. vol 27, no 2, 507-531. |
Jul 10 |
comment |
Kalinin's formulation of the Anosov closing lemma
Guess you meant: The point $y$ is obtained by taking the intersection of the local stable set of $p$ with the nth pull-back of the local unstable set of $f^n(x)$. |
May 5 |
revised |
Generalizations and relative applications of Fekete's subadditive lemma
Allow infinity values. |
Apr 9 |
comment |
Rationality of translation lengths in hyperbolic groups
@lee-mosher Is it really true that "the expression d(1,g^n)/n achieves its limit at some finite value n=N independent of g"? In the free group of two generators a, b, if g=bab^{-1} then d(1,g^n)/n=(n+2)/n. Am I missing something stupid? Or is it necessary to replace g by an appropriate conjugate element? |
Mar 24 |
comment |
Continuous maps which send intervals of $\mathbb{R}$ to convex subsets of $\mathbb{R}^2$
This is the Mihalik-Wieczorek problem. It's indeed devilish. :) Let me remark that if you only ask for the convexity of $f(I)$ for the intervals of the form $I=[0,t]$ then it is possible to construct a space-filling curve: see arxiv.org/abs/1407.5204 and the references there. |
Mar 19 |
awarded | Explainer |
Mar 18 |
answered | A metric for Grassmannians |
Mar 18 |
awarded | Excavator |
Mar 18 |
awarded | Organizer |
Mar 18 |
revised |
A metric for Grassmannians
Added tags |
Mar 18 |
suggested | approved edit on A metric for Grassmannians |
Mar 18 |
comment |
A metric for Grassmannians
@RyanBudney The Riemannian metric from your second suggestion is explicitly described in this 1967 paper pnas.org/content/57/3/589.full.pdf+html which also describes geodesics and other interesting stuff. |
Mar 18 |
comment |
A metric for Grassmannians
@IanMorris Let me consider a variation of one of Ryan's suggestions: If we metrize the projective space using the sine of the angle, and regard the planes V, W as subsets of the projective space, then the Hausdorff distance between them is exactly Ian's distance. Using this interpretation, Ian's discovery that the two maxima in his formula coincide become a corollary of the fact that there exists an isometry of the ambient space that switches V and W (see math.stackexchange.com/questions/118873/…). |
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 |