论文标题
Bernoulli变量，经典排除过程和自由概率
Bernoulli variables, classical exclusion processes and free probability
论文作者
论文摘要
我们通过利用其与量子对称简单排除过程并使用自由概率中的工具来利用其连接，对经典对称简单排除过程的已知大偏差函数的新描述。这似乎似乎是悖论，因为自由概率通常涉及非交换概率，而简单的排除过程属于经典概率领域。在途中，我们为相关的伯努利变量的自由能提供了一个新的公式 - 别名 - 概率分布的拉普拉斯变换的对数，以其非统一指数的累积量。后一个结果是通过为随机变量累积的组合方法或Feynman图借用技术的累积方法而获得的。
We present a new description of the known large deviation function of the classical symmetric simple exclusion process by exploiting its connection with the quantum symmetric simple exclusion processes and using tools from free probability. This may seem paradoxal as free probability usually deals with non commutative probability while the simple exclusion process belongs to the realm of classical probability. On the way, we give a new formula for the free energy -- alias the logarithm of the Laplace transform of the probability distribution -- of correlated Bernoulli variables in terms of the set of their cumulants with non-coinciding indices. This latter result is obtained either by developing a combinatorial approach for cumulants of products of random variables or by borrowing techniques from Feynman graphs.
