461 reputation
216
bio website mat.uc.cl/~jairo.bochi
location Santiago, Chile
age 40
visits member for 5 years, 9 months
seen Jul 31 at 14:46

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