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bio website ttic.uchicago.edu/~yury
location Chicago, IL
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visits member for 2 years, 3 months
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Sep
30
awarded  Explainer
Sep
28
comment Relationship between 2 L-p spaces
Hint: (1) use that $f$ is bounded, (2) prove that for every bounded $f$, there exists $C$ such that $|f(x)|^{p_2} \leq C |f(x)|^{p_1}$ for every $x$.
Sep
28
comment Relationship between 2 L-p spaces
For this statement to be true, we should have $p_1 \leq p_2$.
Sep
28
comment Relationship between 2 L-p spaces
This is false if $f$ is bounded and $\mu(E) = \infty$. Consider $f(x) = 1$. We have, $f\in L_{p_1}({\mathbb R})$ for $p_1=\infty$, but $f\notin L_{p_2}({\mathbb R})$ for $p_2 = 1<p_1$.
Jul
14
awarded  Yearling
Mar
16
comment Difference between $A\to B\to C$ and $A\to(B\to C)$
Or cs.nott.ac.uk/~txa/g52ifr/html/Prop.html : “Implication is right associative, i.e. we read P -> Q -> R as P -> (Q -> R).”
Mar
16
comment Difference between $A\to B\to C$ and $A\to(B\to C)$
See e.g. springer.com/cda/content/document/cda_downloaddocument/… : “Although the implication operator is assumed to be right associative, so that $p \to q \to r$ unambiguously means $p \to (q \to r)$, we will write the formula with parentheses to avoid confusion with $(p\to q)\to r$.”
Mar
16
answered Difference between $A\to B\to C$ and $A\to(B\to C)$
Mar
16
revised On the importance of independence in the central limit theorem
added 187 characters in body
Mar
16
answered On the importance of independence in the central limit theorem
Feb
18
revised Estimating certain order statistics of a set.
added the normalization factor k/n to the formula for E[Y]
Feb
18
answered Estimating certain order statistics of a set.
Feb
1
reviewed Approve suggested edit on Prove that $\sum_{k=1}^{n}\binom{n}{k}=\sum_{k=0}^{n-1}2^{k}$
Feb
1
comment Random walk on $\mathbb{Z}$ with more than two possible steps
Sounds good. Regarding question 2, even if $A=\{-1,1\}$ and $p_{-1} > p_1$, we have $\lambda_1=1$ and $\lambda_2 > 1$. Consider another example: $A=\{-3,-1,2\}$ and $p_{-3} = 1/4$, $p_{-1} = 1/4$, and $p_2 = 1/2$. Then values of $\lambda$ are given by $\lambda^{-2}/2 + \lambda/4 + \lambda^3/4 = 1$. The roots of this equation have absolute values approximately 1, 0.6388969200, and 1.769292354 (some are equal to 1, some are greater than 1, and some are less than 1).
Feb
1
comment Random walk on $\mathbb{Z}$ with more than two possible steps
(1) I don't understand your formula. What is the event $a=-1$? When does it happen? (2) The expression $A \lambda_1^k + B \lambda_2^k$ is unbounded (either when $k > 0$, or $k < 0$, or both) unless $A \lambda_1^k + B \lambda_2^k \equiv 1$.
Feb
1
comment Random walk on $\mathbb{Z}$ with more than two possible steps
How did you get the recurrence relation? The random walk might visit point $k-1$ many times; each time it visits $k-1$, there is a chance that it will go to point $k$. Also is $k$ a positive integer? If not, your formula might give values greater than 1 for $\tilde p_k$ (which doesn't make any sense).
Jan
28
answered A random variable with neither probability density function nor probability mass function… is this example wrong?
Jan
27
awarded  Enlightened
Jan
27
awarded  Nice Answer
Jan
24
answered Why is $E(X^2)$ not equal to the sum of $(x^2 \cdot P(x^2))$ instead of $x^2 \cdot P(x)$