= Solution
A <Markov kernel> $K$ with <stationary distribution> $\pi$ is <geometric ergodicity>[geometrically ergodic] if there are $\rho<1$ and a finite function $M(x)$ such that
$$
\lVert K^m(x,\mathord\cdot)-\pi\rVert_{\mathrm{TV}}
\leq M(x)\rho^m
$$
for every $m\geq0$ and almost every starting point $x$, where $\lVert\cdot\rVert_{\mathrm{TV}}$ is <total variation distance>.
A measurable set $A$ is a <small set> with minorisation constant $\alpha>0$ if some integer $r\geq1$ and some <probability measure> $\nu$ satisfy
$$
K^r(x,B)\geq\alpha\nu(B)
$$
for every $x\in A$ and every measurable $B$.
A standard <drift-minorisation condition> is that the chain be <irreducible Markov chain>[irreducible] and <aperiodic Markov chain>[aperiodic], and that there exist a measurable $V\geq1$, a small set $A$, constants $\lambda<1$ and $b<\infty$ such that
$$
KV(x)\leq\lambda V(x)+b\mathbf1_A(x).
$$
These conditions imply geometric ergodicity.
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