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- W3127399890 abstract "On a large class of infinite trees <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=application/x-tex>T</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove the existence of harmonic functions <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=h> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding=application/x-tex>h</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, with respect to suitable transient transition operators <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding=application/x-tex>P</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, that satisfy the following universal property: <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=h> <mml:semantics> <mml:mi>h</mml:mi> <mml:annotation encoding=application/x-tex>h</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is the Poisson transform of a martingale on the end-point boundary <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega> <mml:semantics> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:annotation encoding=application/x-tex>Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper T> <mml:semantics> <mml:mi>T</mml:mi> <mml:annotation encoding=application/x-tex>T</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (equipped with the harmonic measure induced by <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper P> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding=application/x-tex>P</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) such that, for every measurable function <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Omega> <mml:semantics> <mml:mi mathvariant=normal>Ω<!-- Ω --></mml:mi> <mml:annotation encoding=application/x-tex>Omega</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, it contains a subsequence converging to <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in measure. Moreover, the martingale visits every open set of measurable functions with positive lower density." @default.
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- W3127399890 date "2021-02-19" @default.
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- W3127399890 title "Frequently dense harmonic functions and universal martingales on trees" @default.
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