The subleading order of two dimensional cover times

By David Belius, N. Kistler. 2014

77 citations recorded by the source corpus.

The $$\varepsilon $$ε-cover time of the two dimensional torus by Brownian motion is the time it takes for the process to come within distance $$\varepsilon >0$$ε>0 from any point. Its leading order in the small $$\varepsilon $$ε-regime has been established by Dembo et al. (Ann Math 160:433–464, 2004). In this work, the second order correction is identified. The approach relies on a multi-scale refinement of the second moment method, and draws on ideas from the study of the extremes of branching Brownian motion.

Subfields: Condensed Matter Physics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a1e8099dca5b92df39d9cf621e80c4f6a979c4d

How researchers see this paper

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In Condensed Matter Physics

1. Zhan Shi
2. L. Arguin
3. P. Bourgade
4. David Belius
5. Thomas Madaule
6. Elie Aidékon
7. Rémi Rhodes
8. Vincent Vargas

In Finance

1. Zhan Shi
2. David Belius
3. L. Arguin
4. P. Bourgade
5. Thomas Madaule

In Mathematical Physics

1. L. Arguin
2. P. Bourgade
3. Zhan Shi
4. David Belius
5. Joseph Najnudel
6. Thomas Madaule
7. Ofer Zeitouni
8. Christian Webb

Citations in the corpus

• Maximum of the Characteristic Polynomial of Random Unitary Matrices (2015, background): “Important non-Gaussian examples include cover times of the twodimensional random walk on the torus whose leading order was determined in [27] and subleading order in [9].”
• Branching random walks (2015, background): “As such, new lights have been recently shed on the cover time of the two-dimensional torus by simple random walk (Ding [95], Belius and Kistler [36]).”
• Extrema of log-correlated random variables: Principles and Examples (2016, background): “We refer the reader to [15,29] for results on this question.”