9 problems

Let $U$ and $V$ be source variables, and let $X$ and $Y$ be target variables. Write $C_{\mathsf{GK}}(U;V)$ for the Gács–Körner common information of $U$ and $V$. A target distribut…

Consider a multiterminal secret key agreement problem with several active users, no helpers, no silent users, and no wiretapper's side information. Let the users observe their resp…

Let $a_i$ and $\alpha_i$, $1\leq i\leq n$, be the parameters appearing in the polynomial equations … where solving the equation for each $a_i$ gives a left root and a right root. R…

Consider the total-variation-distance version of Wyner's common information for a source $(X,Y)$ whose alphabet is countably infinite or uncountable. The exponential strong convers…

Let $P_WP_{X|W}P_{Y|W}$ be a joint distribution in which $X$ and $Y$ are conditionally independent given $W$, and let $\widehat{C}_{\mathrm{Wyner}}(\pi_{XY})$ and…

Let $C_{\operatorname{S}}(0)$ denote the secrecy capacity when the total public discussion rate is asymptotically zero, and let $J_{\operatorname{GK}}(\mathbf{Z}_V)$ denote the mul…

Common-information invariance conjecture. Any common information remains unchanged when each variable is replaced by its sufficient statistic about the other variables.

Let $X$, $Y$, and $Z$ be jointly distributed random variables, and let $C_{GK}(X;Y|Z)$ denote their conditional Gács–Körner common information. A conditional Gács–Körner secret-key…

Let $m_1$, $m_2$, and $m_3$ be information elements, and write $m_{ij}$ and $m_{123}$ for their common information elements indexed by the corresponding subsets. Supermodularity co…