题目：A noncommutative de Finetti theorem for Boolean independence

　　报告人：刘伟华 博士(美国加州大学伯克利分校)

　　时间：2014年5月19日(星期一)下午14:00-15:00

　　地点：浙江大学玉泉校区工商楼二楼数学演讲厅

　　Abstract：In the noncommutative probability theory, Speicher showed that there are two unital universal products: the tensor product and the free product. These two products correspond to the classical independence and Voiculuscu’s free independence respectively. In the classical probability theory, de Finetti theorem plays an important role in probabilistic symmetries. The theorem states that an infinite family of random variables whose joint distribution is invariant under finite permutations are conditionally independent and identically distributed. In 2009, Kostler and Speicher proved a de Finetti type theorem for free independence by using the Wang’s quantum permutation groups and their coactions on the joint distribution of a sequence of random variables. Besides the two unital products, there is another unique non-unital product, which is called Boolean product. The Boolean product also defines an independent relation which is called Boolean independence. Our work here is to give a de Finetti type theorem for Boolean independence. We will introduce a family of quantum semigroups and their coactions on noncommutative polynomials. Then, we define an invariance condition for the joint distribution of an infinite sequence of random variables. We will show that the joint distribution of a sequence of random variables satisfies the invariance condition is equivalent to the fact that the sequence of random variables are identically distributed and boolean independent with respect to the conditional expectation onto their tail algebra.

　　刘伟华博士简介: 2004年保送进入浙江大学竺可桢学院混合班，2010年7月获浙江大学数学硕士学位，2010年12月在华人数学家大会上获得新世界数学硕士论文金奖，2010年9月赴美国加州大学伯克利分校攻读博士学位，导师为美国科学院院士、自由概率论创始人 Dan V. Voiculescu 教授.