We study a fragmentation of the $\mathbf p$-trees of Camarri and Pitman[Elect. J. Probab., vol. 5, pp. 1--18, 2000]. We give exact correspondencesbetween the $\mathbf p$-trees and trees which encode the fragmentation. We thenuse these results to study the fragmentation of the ICRTs (scaling limits of$\mathbf p$-trees) and give distributional correspondences between the ICRT andthe tree encoding the fragmentation. The theorems for the ICRT extend the onesby Bertoin and Miermont [Ann. Appl. Probab., vol. 23(4), pp. 1469--1493, 2013]about the cut tree of the Brownian continuum random tree.
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机译:我们研究了Camarri和Pitman [Elect。]的$ \ mathbf p $-树的碎片。 J.Probab。,第一卷。 5,第1--18页,2000年]。我们给出$ \ mathbf p $-树和编码碎片的树之间的确切对应关系。然后,我们使用这些结果来研究ICRT的碎片(标度限制为\\ mathbf p $ -trees),并给出ICRT与编码碎片的树之间的分布对应关系。 ICRT的定理扩展了Bertoin和Miermont的定理。应用Probab。,第一卷23(4),第1469--1493页,2013]关于布朗连续体随机树的割树。
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