# Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation: one sided travelling-waves

@article{Harris2006FurtherPA, title={Further probabilistic analysis of the Fisher–Kolmogorov–Petrovskii–Piscounov equation: one sided travelling-waves}, author={J. W. Harris and Simon R. Harris and Andreas E. Kyprianou}, journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques}, year={2006}, volume={42}, pages={125-145} }

## 56 Citations

### Survival of Near-Critical Branching Brownian Motion

- Mathematics
- 2011

Consider a system of particles performing branching Brownian motion with negative drift $\mu= \sqrt{2 - \varepsilon}$ and killed upon hitting zero. Initially there is one particle at x>0. Kesten…

### Branching Brownian motion with selection

- Mathematics
- 2012

In this thesis, branching Brownian motion (BBM) is a random particle system where the particles diffuse on the real line according to Brownian motions and branch at constant rate into a random number…

### A Strong Law of Large Numbers for Super-Critical Branching Brownian Motion with Absorption

- MathematicsJournal of Statistical Physics
- 2020

We consider a (one-dimensional) branching Brownian motion process with a general offspring distribution having at least two moments, and in which all particles have a drift towards the origin where…

### Yaglom-type limit theorems for branching Brownian motion with absorption

- Mathematics
- 2020

We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the…

### Spine proofs for Lp-convergence of branching-diffusion martingales

- Mathematics
- 2006

Using the foundations laid down in Hardy and Harris (2006) ["A new formulation of the spine approach in branching diffusions", arXiv:math.PR/0611054], we present new spine proofs of the…

### Speed and fluctuations of N-particle branching Brownian motion with spatial selection

- Mathematics
- 2016

We consider branching Brownian motion on the real line with the following selection mechanism: every time the number of particles exceeds a (large) given number N, only the N right-most particles are…

### Genealogy of extremal particles of branching Brownian motion

- Mathematics
- 2010

Branching Brownian motion describes a system of particles that diffuse in space and split into offspring according to a certain random mechanism. By virtue of the groundbreaking work by M. Bramson on…

### Velocity of the $L$-branching Brownian motion

- Mathematics
- 2015

We consider a branching-selection system of particles on the real line that evolves according to the following rules: each particle moves according to a Brownian motion during an exponential lifetime…

### Branching Brownian motion in an expanding ball and application to the mild obstacle problem

- Mathematics
- 2021

We first consider a d-dimensional branching Brownian motion (BBM) evolving in an expanding ball, where the particles are killed at the boundary of the ball, and the expansion is subdiffusive in time.…

### Branching Brownian motion seen from its tip

- Mathematics
- 2011

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 (e.g. from its rightmost particle) converges to an…

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