在過去幾年中，無限維分析和量子概率領域得到了日益顯著的發展，并發現了許多新的應用，特別是在古典概率和物理的不同分支中。這些領域的一流論文數量也以同樣的速度增長。這是目前唯一一本專門研究這些領域的期刊。它為被吸引到這些領域的大量數學家、數學物理學家和其他科學家提供了一個必不可少的和中心的參考點。這兩個領域都具有很強的跨學科性質，與經典概率論、隨機分析、數學物理、算子代數、不可逆性、遍歷理論與動力系統、量子群、經典與量子隨機幾何、量子混沌、狄利克雷形式、調和分析、量子測量、量子計算機等有著深刻的聯系。該雜志反映了這種跨學科性，并歡迎在所有這些相關領域的高質量論文，特別是那些揭示了與該雜志的主要領域的聯系的論文。這本雜志的主要目的是提供一個最新的概述，在其領域的最新的能力。專門討論當前特別感興趣的單一主題的特刊也將在本刊發表。

In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields.It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.The principal objective of this journal is to provide an up-to-date overview of the state-of-the-art in its fields of competence.Special issues devoted to single topic of particular current interest will also be published in this journal.