Shannon's problem on the monotonicity of entropy and a Conjecture of Tao

Ziran Liu

Let $X_1,X_2,\dots$ be i.i.d. finitely supported random variables in a torsion-free abelian group, and write $S_k=X_1+\cdots +X_k$, and $H(S_k)$ is the Shannon entropy $S_k$, for a…