Freezing and Decorated Poisson Point Processes
By Eliran Subag, Ofer Zeitouni. 2014
57 citations recorded by the source corpus.
The limiting extremal processes of the branching Brownian motion (BBM), the two-speed BBM, and the branching random walk are known to be randomly shifted decorated Poisson point processes (SDPPP). In the proofs of those results, the Laplace functional of the limiting extremal process is shown to satisfy $${L\left[\theta_{y}f\right]=g\left(y-\tau_{f}\right)}$$Lθyf=gy-τf for any nonzero, nonnegative, compactly supported, continuous function f, where $${\theta_{y}}$$θy is the shift operator, $${\tau_{f}}$$τf is a real number that depends on f, and g is a real function that is independent of f. We show that, under some assumptions, this property characterizes the structure of SDPPP. Moreover, when it holds, we show that g has to be a convolution of the Gumbel distribution with some measure.The above property of the Laplace functional is closely related to a ‘freezing phenomenon’ that is expected to occur in a wide class of log-correlated fields, and which has played an important role in the analysis of various models. Our results shed light on this intriguing phenomenon and provide a natural tool for proving an SDPPP structure in these and other models.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0bbbc19ecc119275ef995e745a8a3e46cf755c9b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Zhan Shi
- Jian Ding
- Ofer Zeitouni
- Rishideep Roy
- Thomas Madaule
- Joseph Najnudel
- David Belius
- Elliot Paquette
In Statistics and Probability
- Jian Ding
- Zhan Shi
- Rishideep Roy
- Ofer Zeitouni
- Thomas Madaule
- Alice Guionnet
- Elie Aidékon
- Noureddine El Karoui
Citations in the corpus
- Convergence of the centered maximum of log-correlated Gaussian fields (2015, methodology): “(We do not discuss in this paper the notion of freezing, referring instead to [15] and to [22].”
- Branching random walks (2015, methodology): “See also Gouéré [117] for an analysis based on [27], [28], [29] and [12], and Subag and Zeitouni [225] for a general view of decorated Poisson point processes.”