All Questions
9 questions
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A measure on the group of homeomorphisms of $\mathbb T^2$
Let us consider the group of measure-preserving homeomorphisms of $\mathbb T^2$ (with transformations identified if they agree almost
everywhere) called $G[\mathbb T^2, \mathcal L^2]$. We shall ...
- 101
1
vote
0
answers
177
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Building random homeomorphisms of the torus $\mathbb T^2$
In https://arxiv.org/abs/0912.3423, a family of random homeomorphisms of the circle is constructed. Main Question: Can the construction be generalized to higher space dimensions, e.g. to $\mathbb T^2$?...
- 101
5
votes
2
answers
389
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Divergence of Green function of random walks at spectral radius
Let $P=(p(x,y))_{x, y\in N}$ be the transition matrix over countable states $N$.
Consider the generating Green function $G(x, y|t)=\sum_{0}^{\infty} p^n(x, y) t^n$, where $p^n(x,y)$ is the $(x,y)$-...
- 619
8
votes
0
answers
211
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Superharmonic functions and amenability
Let $G$ be a group generated by a finite set $S$. Let $P$ be a Markov operator defined by the uniform measure on $S$. A function is superharmonic if $Pf\leq f$.
Assume that there is a set of non-...
- 4,705
9
votes
3
answers
654
views
measure with given push-forwards
Let $X,Y$ be locally compact spaces (in my specific case, they are locally compact groups). Suppose that we are given a measure $\mu$ on $X$ and a finite number of quotient maps $p_1,\ldots,p_n:Y\...
23
votes
2
answers
7k
views
What is a Gaussian measure?
Let $X$ be a topological affine space. A Gaussian measure on $X$ is characterized by the property that its finite-dimensional projections are multivariate Gaussian distributions.
Is there a direct ...
- 8,512
18
votes
1
answer
996
views
Existance of certain almost invariant functions related to amenability and piece-wise transformations
We would like very much to know the answer to the following question:
Let $\|\cdot\|$ be any norm on $\mathbb{Z}^d$ and let $W(\mathbb{Z}^d)$ be the group of all bijections of $\mathbb{Z}^d$ such ...
6
votes
0
answers
295
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Is there an idempotent measure on the free LD system?
This is a follow up question to MO question "Idempotent measures on the free binary system?".
Let $(A,*)$ be the free binary operation on one generator which satisfies the left self distributive law:
...
- 3,547
13
votes
1
answer
736
views
Idempotent measures on the free binary system?
Let $(S,*)$ be the free (non associative) binary system on one generator (so $S$ is just the set of terms in $*$ and $1$). There is an extension of $*$ to the space $P(S)$ of finitely additive ...
- 3,547