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We study a version of first passage percolation on $\mathbb{Z}^d$ where the random passage times on the edges are replaced by contact times represented by random closed sets on $\mathbb{R}$. Similarly to the contact process without recovery, an infec
Externí odkaz:
http://arxiv.org/abs/2412.14987
We study internal diffusion limited aggregation on $\mathbb{Z}$, where a cluster is grown by sequentially adding the first site outside the cluster visited by each random walk dispatched from the origin. We assume that the increment distribution $X$
Externí odkaz:
http://arxiv.org/abs/2411.10113
This paper presents a comprehensive review of stochastic processes, with a particular focus on Markov chains and jump processes. The main results related to queuing systems are analyzed. Additionally, conditions that ensure the stability, or ergodici
Externí odkaz:
http://arxiv.org/abs/2409.10735
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distribution of the time in these states may differ. In this sense, the process is asymmetric, and this paper extends previou
Externí odkaz:
http://arxiv.org/abs/2409.05641
Autor:
Martinez-Rodriguez, Carlos
This document presents a compilation of results related to the theory of stochastic processes, with a specific focus on Markov processes, regenerative processes, renewal processes, and stationary processes. The relevance of these topics lies in the a
Externí odkaz:
http://arxiv.org/abs/2408.01012
We give a short proof of a recent result of Claesson, Dukes, Frankl\'in and Stef\'ansson, that connects tournament score sequences and the Erd\H{o}s-Ginzburg-Ziv numbers from additive number theory. We show that this connection is, in fact, an instan
Externí odkaz:
http://arxiv.org/abs/2407.01441
Autor:
Hermann, Felix, Casanova, Adrián Gonzalez, Santos, Renato Soares dos, Tóbiás, András, Wakolbinger, Anton
We consider a population whose size $N$ is fixed over the generations, and in which random beneficial mutations arrive at a rate of order $1/\log N$ per generation. In this so-called Gerrish-Lenski regime, typically a finite number of contending muta
Externí odkaz:
http://arxiv.org/abs/2407.00793
A sequence $d_1\le\cdots\le d_n$ is graphical if it is the degree sequence of a graph. Balister, the second author, Groenland, Johnston and Scott showed that there are asymptotically $C4^n/n^{3/4}$ such sequences. However, the constant $C$ involves a
Externí odkaz:
http://arxiv.org/abs/2406.05110
Autor:
Soni, Ritik, Pathak, Ashok Kumar
In this paper, we define a compound generalized fractional counting process (CGFCP) which is a generalization of the compound versions of several well-known fractional counting processes. We obtain its mean, variance, and the fractional differential
Externí odkaz:
http://arxiv.org/abs/2405.11033
Autor:
Campos, Alberto M.
This paper introduces a new type of covering process that covers the set of natural numbers using renewal processes as objects. Inspired by the behavior of prime numbers, the model in each step finds the smallest vacant point, $k$, and place, startin
Externí odkaz:
http://arxiv.org/abs/2405.05793