کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590305 1334947 2014 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Semicircular limits on the free Poisson chaos: Counterexamples to a transfer principle
ترجمه فارسی عنوان
محدودیت نیمکره ای در هرج و مرج پوآسون آزاد: نمونه هایی از اصل انتقال است
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We establish a class of sufficient conditions ensuring that a sequence of multiple integrals with respect to a free Poisson measure converges to a semicircular limit. We use this result to construct a set of explicit counterexamples showing that the transfer principle between classical and free Brownian motions (recently proved by Kemp, Nourdin, Peccati and Speicher (2012)) does not extend to the framework of Poisson measures. Our counterexamples implicitly use kernels appearing in the classical theory of random geometric graphs. Several new results of independent interest are obtained as necessary steps in our analysis, in particular: (i) a multiplication formula for free Poisson multiple integrals, (ii) diagram formulae and spectral bounds for these objects, and (iii) a counterexample to the general universality of the Gaussian Wiener chaos in a classical setting.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 267, Issue 4, 15 August 2014, Pages 963–997
نویسندگان
, ,