Gaussian multiplicative chaos and applications: a review
R Rhodes, V Vargas - 2014 - projecteuclid.org
In this article, we review the theory of Gaussian multiplicative chaos initially introduced by
Kahane's seminal work in 1985. Though this beautiful paper faded from memory until …
Kahane's seminal work in 1985. Though this beautiful paper faded from memory until …
Everything is a race and nakamoto always wins
Nakamoto invented the longest chain protocol, and claimed its security by analyzing the
private double-spend attack, a race between the adversary and the honest nodes to grow a …
private double-spend attack, a race between the adversary and the honest nodes to grow a …
[图书][B] Branching random walks
Z Shi - 2015 - Springer
These notes attempt to provide an elementary introduction to the one-dimensional discrete-
time branching random walk and to exploit its spinal structure. They begin with the case of …
time branching random walk and to exploit its spinal structure. They begin with the case of …
Critical Gaussian multiplicative chaos: a review
E Powell - arXiv preprint arXiv:2006.13767, 2020 - arxiv.org
arXiv:2006.13767v3 [math.PR] 2 Jul 2020 Page 1 arXiv:2006.13767v3 [math.PR] 2 Jul 2020
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …
Branching Brownian motion seen from its tip
E Aïdékon, J Berestycki, É Brunet, Z Shi - Probability Theory and Related …, 2013 - Springer
It has been conjectured since the work of Lalley and Sellke (Ann. Probab., 15, 1052–1061,
1987) that branching Brownian motion seen from its tip (eg from its rightmost particle) …
1987) that branching Brownian motion seen from its tip (eg from its rightmost particle) …
Maximum of the characteristic polynomial of random unitary matrices
It was recently conjectured by Fyodorov, Hiary and Keating that the maximum of the
characteristic polynomial on the unit circle of a N * NN× N random unitary matrix sampled …
characteristic polynomial on the unit circle of a N * NN× N random unitary matrix sampled …
The extremal process of branching Brownian motion
We prove that the extremal process of branching Brownian motion, in the limit of large times,
converges weakly to a cluster point process. The limiting process is a (randomly shifted) …
converges weakly to a cluster point process. The limiting process is a (randomly shifted) …
Critical Gaussian multiplicative chaos: convergence of the derivative martingale
In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the
so-called derivative martingale, introduced in the context of branching Brownian motions …
so-called derivative martingale, introduced in the context of branching Brownian motions …
On the maximum of the CE field
In this article, we investigate the extremal values of (the logarithm of) the characteristic
polynomial of a random unitary matrix whose spectrum is distributed according to the …
polynomial of a random unitary matrix whose spectrum is distributed according to the …
Convergence in law of the maximum of the two‐dimensional discrete Gaussian free field
M Bramson, J Ding, O Zeitouni - Communications on Pure and …, 2016 - Wiley Online Library
Convergence in Law of the Maximum of the Twoâ•’Dimensional Discrete Gaussian Free Field
Page 1 Convergence in Law of the Maximum of the Two-Dimensional Discrete Gaussian Free …
Page 1 Convergence in Law of the Maximum of the Two-Dimensional Discrete Gaussian Free …