Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A basic problem in information theory is the following: Let $\mathbf{P} = (\mathbf{X}, \mathbf{Y})$ be an arbitrary distribution where the marginals $\mathbf{X}$ and $\mathbf{Y}$ are (potentially) correlated. Let Alice and Bob be two players where Alice gets samples $\{x_i\}_{i \ge 1}$ and Bob gets samples $\{y_i\}_{i \ge 1}$ and for all $i$, $(x_i, y_i) \sim \mathbf{P}$. What joint distributions $\mathbf{Q}$ can be simulated by Alice and Bob without any interaction? #R##N#Classical works in information theory by G{\'a}cs-K{\"o}rner and Wyner ansr this question when at least one of $\mathbf{P}$ or $\mathbf{Q}$ is the distribution on $\{0,1\} \times \{0,1\}$ where each marginal is unbiased and identical. Hover, other than this special case, the ansr to this question is understood in very few cases. Recently, Ghazi, Kamath and Sudan shod that this problem is decidable for $\mathbf{Q}$ supported on $\{0,1\} \times \{0,1\}$.  extend their result to $\mathbf{Q}$ supported on any finite alphabet. #R##N# rely on recent results in Gaussian geometry (by the authors) as ll as a new \emph{smoothing argument} inspired by the method of \emph{boosting} from learning theory and potential function arguments from complexity theory and additive combinatorics.
['Anindya De', 'Elchanan Mossel', 'Joe Neeman']
I am writing a research paper on a idea Non interactive simulation of correlated distributions is decidable
[{"from": "human", "value": "I am writing a research paper on a idea Non interactive simulation of correlated distributions is decidable"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A basic problem in information theory is the following: Let $\\mathbf{P} = (\\mathbf{X}, \\mathbf{Y})$ be an arbitrary distribution where the marginals $\\mathbf{X}$ and $\\mathbf{Y}$ are (potentially) correlated. Let Alice and Bob be two players where Alice gets samples $\\{x_i\\}_{i \\ge 1}$ and Bob gets samples $\\{y_i\\}_{i \\ge 1}$ and for all $i$, $(x_i, y_i) \\sim \\mathbf{P}$. What joint distributions $\\mathbf{Q}$ can be simulated by Alice and Bob without any interaction? #R##N#Classical works in information theory by G{\\'a}cs-K{\\\"o}rner and Wyner ansr this question when at least one of $\\mathbf{P}$ or $\\mathbf{Q}$ is the distribution on $\\{0,1\\} \\times \\{0,1\\}$ where each marginal is unbiased and identical. Hover, other than this special case, the ansr to this question is understood in very few cases. Recently, Ghazi, Kamath and Sudan shod that this problem is decidable for $\\mathbf{Q}$ supported on $\\{0,1\\} \\times \\{0,1\\}$.  extend their result to $\\mathbf{Q}$ supported on any finite alphabet. #R##N# rely on recent results in Gaussian geometry (by the authors) as ll as a new \\emph{smoothing argument} inspired by the method of \\emph{boosting} from learning theory and potential function arguments from complexity theory and additive combinatorics."}]