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Let's play a game. I start with $N$ indistinguishable tokens, and I wait $T$ turns. Every turn, each token has probability $p$ of disappearing. I want an analytic formula for the entropy of this ...

Assume a distribution $\pi \propto e^{-f}$ satisfies log-Sobolev inequality (LSI) $$\forall \rho \in P(\mathbb{R}^n), \quad KL(\rho\| \pi) \le \frac{1}{2\lambda} I(\rho \| \pi)$$ with LSI constant $\...

I have $n$ IID Bernoulli random variables denoted by $X_1,X_2,\ldots X_n$ with parameter $p$. I am interested in knowing if the following inequality involving mutual information holds : $\boxed{\max_{...

Let $X_1, \dots, X_n, Y$ be random variables, each taking values in $\{0,1\}$. Assume that we are interested in estimating, for each $v=(v_1,\dots,v_n)\in \{0,1\}^n$, the probability $$ p(v) = P[Y=1|...