Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMulti-Scaling of the $n$-point density function for coalescing Brownian motions
81
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This paper gives a derivation for the large time asymptotics of the $n$-point density function of a system of coalescing Brownian motions on $bf{R}$.
rate research
Read More
We consider a family of free multiplicative Brownian motions $b_{s,tau}$ parametrized by a positive real number $s$ and a nonzero complex number $tau$ satisfying $leftvert tau-srightvert leq s,$ with an arbitrary unitary initial condition. We compute the Brown measure $mu_{s,tau}$ of $b_{s,tau}$ and find that it has a simple structure, with a density in logarithmic coordinates that is constant in the $tau$-direction. We also find that all the Brown measures with $s$ fixed and $tau$ varying are related by pushforward under a natural family of maps. Our results generalize those of Driver-Hall-Kemp and Ho-Zhong for the case $tau=s.$ We use a version of the PDE method introduced by Driver-Hall-Kemp, but with some significant technical differences.
We study a natural continuous time version of excited random walks, introduced by Norris, Rogers and Williams about twenty years ago. We obtain a necessary and sufficient condition for recurrence and for positive speed. This is analogous to results for excited (or cookie) random walks.
The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by an alternating renewal process. Bounds to the first-passage-time density and distribution function are obtained, and a simulation procedure to estimate first-passage-time densities is constructed. Examples of applications to problems in environmental sciences and mathematical finance are also provided.
We prove the existence of the intersection local time for two independent, d -dimensional fractional Brownian motions with the same Hurst parameter H. Assume d greater or equal to 2, then the intersection local time exists if and only if Hd<2.
Let $mathbb{T}^d_N$, $dge 2$, be the discrete $d$-dimensional torus with $N^d$ points. Place a particle at each site of $mathbb{T}^d_N$ and let them evolve as independent, nearest-neighbor, symmetric, continuous-time random walks. Each time two particles meet, they coalesce into one. Denote by $C_N$ the first time the set of particles is reduced to a singleton. Cox [6] proved the existence of a time-scale $theta_N$ for which $C_N/theta_N$ converges to the sum of independent exponential random variables. Denote by $Z^N_t$ the total number of particles at time $t$. We prove that the sequence of Markov chains $(Z^N_{ttheta_N})_{tge 0}$ converges to the total number of partitions in Kingmans coalescent.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
