# Questions tagged [probabilistic-method]

Probabilistic methods prove existence results in a nonconstructive fashion, by showing the chance of randomly selecting a solution is greater than zero.

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### Existence of (near) equidistant codewords

My question is originally related to coding theory, but fairly easy to state in pure combinatorial way. Fix $k\in\mathbb{N}$, $\beta\in(0,1)$ and consider the binary cube $\Sigma_n = \{0,1\}^n$ ...
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### Why subcopula is less used in modelling?

I don't know if it is a good idea to post my question in MathOverflow instead of Mathexchange. But it seems to me that it is more appropriate to post my question in MathOverflow. By definition, copula ...
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### Counting progressions for Ramsey-type number

I'm currently learning about Ramsey theory and how to use the probabilistic method to find lower bounds. Currently I'm looking at a family, which I'll call $H$, that is composed of the following ...
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### An extremal combinatorics problem involving column summation

Given $n\in\Bbb N$, $\alpha>0$, $\beta\in\big[\frac12,1\big]$ denote $\mathcal R_{n,\alpha,\beta}$ as collection of all $2^n\times 2^{n^\alpha}$ $0/1$ matrices with every row summing to strictly ... 2k views

### What are fun elementary subjects in probability?

I have to read several lectures on probability or applications of probability for high school students (of high level). There is no necessary part I must lecture, that is, my aim is just advertisement....
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### Does $|A+A|$ concentrate near its mean?

Fix $N$ to be a large prime. Let $A \subset \mathbb{Z}/N\mathbb{Z}$ be a random subset defined by $\mathbb{P}(a \in A) = p$, where $p = N^{-2/3 + \epsilon}$ for some fixed $\epsilon > 0$. My ...
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### Derandomization barriers in complexity theory applicable as barriers to constructive arguments replacing probabilistic method

The probabilistic method as first pioneered by Erdős (although others used this before) shows existence of a certain object while finding that object may take exponential time. (1) Is there any ...
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### List of proofs where existence through probabilistic method has not been constructivised

The probabilistic method as first pioneered by Erdős (although others have used this before) shows the existence of a certain object. What are some of the most important objects for which we can show ...
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### Assigning random orientation to an edge in a regular graph

Given a simple regular graph of degree $d$ on $n$ vertices. Assume an ordering of vertices and assume all orientations of edges is from $i$ to $j$ if edges $ij$ exists and $i<j$. Pick $m$ random ... ### Maximal number of subsets in $\{1,\dots,n\}$ such that neither is contained in a union of two others
What are known estimates for maximal $M$ for which their exists subsets $A_1,\dots,A_M$ in $\{1,\dots,n\}$ such that there do not exist different indexes $i,j,k$ for which $A_i\subset A_j\cup A_k$? ...