Semigroup real characters generated by quasicharacters

Abstract Let S be an infinite, finitely generated semigroup, endowed with a probability measure. Based on the work [A. Erschler and A. Karlsson, Homomorphisms to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>ℝ</m:mi> </m:math> \mathbb{R} constructed from random walks, Ann. Inst. Fourier (Grenoble) 60 2010, 6, 2095–2113], we construct a real character of S using a random walk approach. In our construction, the word length used in Erschler and Karlsson’s work is replaced by a quasicharacter.