Boson and Fermion Brownian Motion

A remark on boson-fermion correspondence

We give a simple explanaition of classical boson-fermion correspondence.

Fermion to Boson Mapping

The enveloping algebra,$D_{n}$,of fermions is extended on the lattice to include the discrete space invariance.This extended algebra,denoted X, has the space symmetry as a factor : $X/D_{n}$ = space group.

临界平面布朗运动环汤中的奇偶性问题（或“自由平面玻色子去了哪里？”）

Parity questions in critical planar Brownian loop-soups (or "where did the free planar bosons go?")

该研究探讨临界二维布朗运动环汤的占据时间场与高斯自由场平方的关联，证明场无法确定环的访问点集，且稠密特殊点属环汤的条件概率为1/2，环分解也分两类各占1/2概率。

Constrained non-crossing Brownian motions, fermions and the Ferrari-Spohn distribution

A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work, we revisit the Ferrari-Spohn model of a Brownian bridge conditioned to avoid a moving wall, which pushes the system into a large-deviation regime. We extend this model to an arbitrary number $N$ of non-crossing Brownian bridges. We obtain the joint distribution of the distances of the Brownian particles from the wall at an intermediate time in the form of the…

Universal fermionization of bosons on permutative representations of the Cuntz algebra ${\cal O}_{2}$

Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra ${\cal O}_{2}$. As examples, we show fermionizations on the Fock space and the infinite wedge.

On a categorical Boson-Fermion correspondence

We propose a categorical version of the Boson-Fermion correspondence and its twisted version. One can view it as a relative of the Frenkel-Kac-Segal construction of quantum affine algebras.