WebMar 24, 2024 · Harmonic functions are called potential functions in physics and engineering. Potential functions are extremely useful, for example, in electromagnetism, where they reduce the study of a 3-component vector field to a 1-component scalar function. A scalar harmonic function is called a scalar potential, and a vector … WebItai Benjamini, Hugo Duminil-Copin, Gady Kozma and Ariel Yadin October 31, 2011 Abstract We study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on Zd. We prove that the vector space of harmonic functions growing at most linearly is d+1-dimensional almost …
Polynomially growing harmonic functions on connected …
WebOct 13, 2016 · In this work we study the structure of finitely generated groups for which a space of harmonic functions with fixed polynomial growth is finite dimensional. It is conjectured that such groups must be virtually nilpotent (the … WebJun 12, 2024 · Polynomially growing harmonic functions on connected groups Idan Perl, Ariel Yadin We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. echolink fusion
Chapter 12 Random walks on groups and random transformations
WebPolynomially growing harmonic functions on connected groups Idan Perl Ben-Gurion University of the Negev, Be’er Sheva ISRAEL Ariel Yadin Abstract. We study the connection between the dimension of certain spaces of harmonic functions on a group and its geometric and algebraic properties. WebOct 25, 2016 · For general groups, vanishing of higher-order discrete derivatives gives a natural notion of polynomial maps, which has been considered by Leibman and others. We provide a simple proof of Alexopoulos's result using this notion of polynomials, under the weaker hypothesis that the space of harmonic functions of polynomial growth of … WebSep 22, 2014 · More recently, Tointon [Toi16] considered functions which are harmonic with respect to weighted measures: if µ : Γ → [0, 1] is a probability measure ( µ (γ) = 1) that is symmetric (µ (γ −1 ) =... compression stocking assist device