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 …

Everything is a race and nakamoto always wins

A Dembo, S Kannan, EN Tas, D Tse… - Proceedings of the …, 2020 - dl.acm.org
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 …

[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 …

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 …

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) …

Maximum of the characteristic polynomial of random unitary matrices

LP Arguin, D Belius, P Bourgade - Communications in Mathematical …, 2017 - Springer
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 …

The extremal process of branching Brownian motion

LP Arguin, A Bovier, N Kistler - Probability Theory and related fields, 2013 - Springer
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) …

Critical Gaussian multiplicative chaos: convergence of the derivative martingale

B Duplantier, R Rhodes, S Sheffield, V Vargas - 2014 - projecteuclid.org
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 …

On the maximum of the CE field

R Chhaibi, T Madaule, J Najnudel - 2018 - projecteuclid.org
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 …

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 …