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bio website math.uvic.ca/faculty/aquas
location University of Victoria
age 47
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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...

1d
comment Minimum number of people such that 2 can be expected to sit next to each other
Just use linearity of expectation - I think this doesn't belong here.
1d
comment binomial coefficients and irrationals
So I'm pretty sure that this has been asked of a lot of people who were unable to prove the weak mixing (of course there is always the chance that it is well known to someone who knows it well, but that this information has not leaked through to the ergodic theorists, but I think this is unlikely).
2d
comment binomial coefficients and irrationals
Very similar questions have arisen in dealing with the "pascal-adic" map. Probably you know this. Karl Petersen likely knows as much as anyone about this.
2d
comment arithmetic progressions with few primes
Is $a_1$ meant to be coprime to $q$? If there is no such requirement, this is trivial. If they are supposed to be coprime, the claim doesn't sound very plausible. I think a more plausible upper bound would be $\lambda (q^\beta/\log(q^\beta))(q/\phi(q))$. Even then I don't see any reason it should be true.
Jul
26
comment Transcendental distance sets
If you believe that all algebraic irrationals are normal numbers, then if you take the set of all real numbers in [0,1] whose decimal digits are 5's and 6's say, then differences of this set are not normal numbers (they have no 3s in their expansion for example) and so cannot be algebraic. On the other hand, you cannot have a positive measure set because differences of positive measure sets contain intervals.
Jul
24
comment How to construct examples of functions in the Spaces of type $\mathcal{S}$
You will need to make your question more accessible and lay out more background if you want to get a reasonable answer.
Jul
20
revised Intersection of two lattices
fix symbol
Jul
20
answered Intersection of two lattices
Jul
20
comment Intersection of two lattices
How could it not be a lattice of full rank? (In particular, $\Lambda$ contains $p\mathbb Z^n$)
Jul
19
comment Entropy, convergence and invariant measures
The standard condition for this to happen is $\bar d(\eta_n,\mu)\to 0$, where $\mu$ is the $(\frac 12,\frac 12)$ Bernoulli measure. The distance $\bar d$ is called the "d-bar" distance. It is described (for example) in Rudolph's book. One definition of $\bar d(\mu,\nu)$ is that is the limit of the minimal integral of $\frac 1n\sum_{i=0}^{n-1}\Delta(x_i,y_i)$ over all couplings of $\mu$ and $\nu$.
Jul
17
comment How to prove that this equation has only one solution?
@Gottfried: Yes exactly. Thanks for the correction.
Jul
17
answered Entropy, Convergence
Jul
17
comment Gradient of Probability Distribution
Aren't there parity issues with your problem? I would think that for the standard lattice, the difference between neighbouring probabilities is the same as the maximum of the two.
Jul
17
comment Invariant and periodic measures of the random dynamical system on the circle generated by $d\theta_t=dW_t$
I think the natural level of generalization is a group extension - or possibly a quotient group extension of a dynamical system. A key property here is that the convolution of Haar measure with anything is Haar measure.
Jul
16
answered Invariant and periodic measures of the random dynamical system on the circle generated by $d\theta_t=dW_t$
Jul
14
revised Invariant and periodic measures of the random dynamical system on the circle generated by $d\theta_t=dW_t$
added 106 characters in body
Jul
14
answered Invariant and periodic measures of the random dynamical system on the circle generated by $d\theta_t=dW_t$
Jul
13
comment Uniform sub-linearity of sub-additive functions on groups
If $G=\mathbb Z$ and $f(n)=|n|$, then $f$ is subadditive. Let $\mu$ be the Dirac measure giving mass $\frac 12$ to $+1$ and $\frac 12$ to $-1$. Then you have (by the strong law of large numbers) that $f(w_n)/n\to 0$ as $n\to\infty$ for almost every $\mathbf w$. But it's not true that there's an $\epsilon$ such that $f(w)\le n\epsilon$ for every word of length $n\ge n_0$.
Jul
12
comment Invariant and periodic measures of the random dynamical system on the circle generated by $d\theta_t=dW_t$
@Julian: It looks to me as though your $\theta$ should be $\theta(\omega)(t)=\omega(t+1)-\omega(1)$, right?
Jul
12
comment Invariant and periodic measures of the random dynamical system on the circle generated by $d\theta_t=dW_t$
@RW: I think the idea is that you take (1) a point; and (2) a 2-sided Brownian motion going through 0. The action is to shift the BM 1 unit to the left; subtract a constant so as to ensure that ensure that the shifted BM goes through 0 (I think this is missing in the Q) and keep track of the shifts that have been made.