bio  website  math.uvic.ca/faculty/aquas 

location  University of Victoria  
age  47  
visits  member for  4 years, 8 months 
seen  1 hour ago  
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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

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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

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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

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binomial coefficients and irrationals
Very similar questions have arisen in dealing with the "pascaladic" map. Probably you know this. Karl Petersen likely knows as much as anyone about this. 
2d

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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 
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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 
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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 
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Intersection of two lattices
How could it not be a lattice of full rank? (In particular, $\Lambda$ contains $p\mathbb Z^n$) 
Jul 19 
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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 "dbar" 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 $\frac 1n\sum_{i=0}^{n1}\Delta(x_i,y_i)$ over all couplings of $\mu$ and $\nu$. 
Jul 17 
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How to prove that this equation has only one solution?
@Gottfried: Yes exactly. Thanks for the correction. 
Jul 17 
answered  Entropy, Convergence 
Jul 17 
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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 
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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 
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Uniform sublinearity of subadditive 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 
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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 
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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 2sided 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. 