Short-time asymptotics for the trace of one- and multi-dimensional Schrödinger semigroups
Short-time asymptotics for the trace of one- and multi-dimensional Schrödinger semigroups
Using Brownian motion we derive the leading asymptotic behaviour, as <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="t down-arrow 0"> <mml:semantics> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo stretchy="false">↓<!-- ↓ --></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">t \downarrow 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, of the (normalized) trace of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="e Superscript t upper L Baseline minus e …