An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture
An Almost Constant Lower Bound of the Isoperimetric Coefficient in the KLS Conjecture
Abstract We prove an almost constant lower bound of the isoperimetric coefficient in the KLS conjecture. The lower bound has the dimension dependency $$d^{-o_d(1)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msub><mml:mi>o</mml:mi><mml:mi>d</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msup></mml:math> . When the dimension is large enough, our lower bound is tighter than the previous best bound which has the dimension dependency $$d^{-1/4}$$ <mml:math …