Convergence of random walks on the circle generated by an irrational rotation
Convergence of random walks on the circle generated by an irrational rotation
Fix <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="alpha element-of left-bracket 0 comma 1 right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\alpha \in [0,1)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Consider the random walk on the circle <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Superscript 1"> <mml:semantics> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> …