Universal Order Statistics of Random Walks

Maxima of Two Random Walks: Universal Statistics of Lead Changes

Occupation Statistics of Critical Branching Random Walks

We consider a critical nearest neighbor branching random walk on the d−dimensional integer lattice. Denote by Vm the maximal number of particles at a single site at time m, and by Gm the event that the branching random walk survives to generation m. We show that if the offspring distribution has finite n-th moment, then in dimensions d ≥ 3, conditional on Gm, Vm = Op(m 1 n ); and if the offspri...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Record statistics for multiple random walks.

We study the statistics of the number of records R(n,N) for N identical and independent symmetric discrete-time random walks of n steps in one dimension, all starting at the origin at step 0. At each time step, each walker jumps by a random length drawn independently from a symmetric and continuous distribution. We consider two cases: (I) when the variance σ(2) of the jump distribution is finit...

Scaling Limits of Coupled Continuous Time Random Walks and Residual Order Statistics through Marked Point Processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forwardor backward-cou...