Đề tài " Branched polymers and dimensional reduction "

We establish an exact relation between self-avoiding branched polymers in D + 2 continuum dimensions and the hard-core continuum gas at negative activity in D dimensions. We review conjectures and results on critical exponents for D + 2 = 2, 3, 4 and show that they are corollaries of our result. We explain the connection (first proposed by Parisi and Sourlas) between branched polymers in D + 2 dimensions and the Yang-Lee edge singularity in D dimensions.