Convergence in law for the branching random walk seen from its tip

Abstract

Considering a critical branching random walk on the real line. In a recent paper, Aidekon [3] developed a powerful method to obtain the convergence in law of its minimum after a log-factor normalization. By an adaptation of this method, we show that the point process formed by the branching random walk and its minimum converge in law to a Poisson point process colored by a certain point process. This result, confirming a conjecture of Brunet and Derrida [10], can be viewed as a discrete analog of the corresponding results for the branching brownian motion, previously established by Arguin et al. [5] [6] and Aidekon et al. [2].

References in corpus (2)

• A branching random walk seen from the tip
• Tightness for a family of recursion equations

Cited by in corpus (8)

• Freezing and decorated Poisson point processes
• Critical Mandelbrot Cascades
• Gaussian multiplicative chaos and applications: a review
• Branching Brownian motion with selection
• Glassy phase and freezing of log-correlated Gaussian potentials
• Towards rigorous analysis of the Levitov-Mirlin-Evers recursion
• On exact scaling log-Infinitely divisible cascades
• The near-critical scaling window for directed polymers on disordered trees