10,103 reputation
12156
bio website math.uvic.ca/faculty/aquas
location University of Victoria
age 47
visits member for 4 years, 9 months
seen 9 mins ago
The pic is the phase portrait of a simple "piecewise isometry". Define a map by sliding the two halves of the plane: the top half to the right; the lower half to the left and then rotate. Around each periodic point of the map there's a "periodic island". These are what are in the image...

1h
comment A Linear Order from AP Calculus
A side comment: The class $\Theta$ is a very small sub-class of the logarithmico-exponential functions studied by Hardy (see also Boshernitzan's work). These have very nice properties including no oscillation: for any two distinct functions in a Hardy Field, eventually $f$ is bigger than $g$ or vice versa.
4h
comment “Edge Density” of Infinite Planar Graphs
My reading was that the vertices of $G$ were not labelled, but that the vertices of the subgraphs were labelled (so that if $G$ is an infinite path, for example, then there are $n!/2$ subgraphs of size $n$).
12h
comment convex hull of the set of permutations with one cycle
I don't think so. For example if the permutation is a transposition, then there are 2 columns and rows with weight 1/2 and the rest with weight 0.
13h
revised convex hull of the set of permutations with one cycle
added 9 characters in body
13h
answered convex hull of the set of permutations with one cycle
14h
comment convex hull of the set of permutations with one cycle
another comment: the $i$th row and the $i$th column have the same sum for each $i$.
14h
comment convex hull of the set of permutations with one cycle
So the matrix with a single 1 somewhere is not in the convex hull. Also the convex hull gives weight 0 to the diagonal, so the convex hull is certainly more complicated than you think.
21h
comment Coupling Marginals of Distributions on the Sphere
You shouldn't expect to be able to do this for atomic distributions. If you had a distribution supported on values whose squares never sum to $n$, you would have a counterexample. The same would be true if the distribution is `almost atomic' (e.g. 99.99% of the mass is within $10^{-100}$ of a collection of values with the above property.
1d
comment Permutations of given length
You're asking to express $n$ as $m_1+\ldots+m_k$ with $m_i\le M_i$
1d
answered $\langle X\rangle_t = t$
1d
comment 2-dimensional sublattices with all vectors having very big square (in absolute value)
Presumably you want your lattice not to be a multiple of any other lattice?
2d
comment A finite field $0$-free restrictive sumset problem
You need $d$ large enough that $(\log m)^d\ge m$. Otherwise any set will contain a set of at most $m$ linearly dependent elements. The form of the dependence (since the base field is $\mathbb F_2$) is exactly $\sum_{v\in S}v=0$.
Aug
24
answered Rajchman measures via strong mixing systems
Aug
22
answered Is there a version of the Titchmarsh Convolution theorem to find singular support?
Aug
21
comment Counting the size of the largest sets of independent strings
Here's an idea for dealing with strings that are not outrageously sparse: take a string, split it up into blocks of length $n/10$, say. For each block, store $\lfloor 10\log_2$(weight)$\rfloor$. If two strings have the same weight vector (and are not ridiculously sparse), then they match. Since there are only $(\log n)^{20}$ weight vectors, this should give a good bound on non-sparse independent sets...
Aug
20
comment A regular variation in infinite ergodic theory
Then taking $A=B=E$ would make this not make sense.
Aug
20
comment Identities and inequalities in analysis and probability
I think this concern is probably too broad to be useful. Maybe I'll wait a while before voting in case people come up with really inspiring answers proving me wrong. At the very least, this should be community wiki.
Aug
20
comment A regular variation in infinite ergodic theory
Probably not very interesting as this would say that if $A$ and $B$ don't intersect initially, they never will. (The identity transformation has this property, but not much else).
Aug
20
comment Algebraically independent matrix invariants
If you've edited the question and made a substantial change, you should indicate in the question what the edits are so that the comments still make sense.
Aug
20
comment Inequality for a gradient of a function in Holder space
Surely this is dimensionaly hopeless: if you halve X, the left side doubles, whereas the right side decreases by a factor of $2^{2N-1}$.