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pro vyhledávání: '"60f15"'
Autor:
Owada, Takashi, Samorodnitsky, Gennady
We extend the classical preferential attachment random graph model to random simplicial complexes. At each stage of the model, we choose one of the existing $k$-simplices with probability proportional to its $k$-degree. The chosen $k$-simplex then fo
Externí odkaz:
http://arxiv.org/abs/2410.17447
Autor:
Kadets, V., Zavarzina, O.
The Strong Law of Large Numbers (SLLN) for random variables or random vectors with different mathematical expectations easily reduces by means of shifts to SLLN for random variables or random vectors whose mathematical expectations are equal to zero.
Externí odkaz:
http://arxiv.org/abs/2410.04832
Autor:
Markering, Maarten
We construct the two-sided infinite self-avoiding walk (SAW) on $\mathbb{Z}^d$ for $d\geq5$ and use it to prove pattern theorems for the self-avoiding walk. We show that infinite two-sided SAW is the infinite-shift limit of infinite one-sided SAW and
Externí odkaz:
http://arxiv.org/abs/2410.01507
We introduce a spatiotemporal self-exciting point process $(N_t(x))$, boundedly finite both over time $[0,\infty)$ and space $\mathscr X$, with excitation structure determined by a graphon $W$ on $\mathscr X^2$. This graphon Hawkes process generalize
Externí odkaz:
http://arxiv.org/abs/2409.16903
Autor:
Kagan, Alexis, Véchambre, Grégoire
We define a family of continuous-time branching particle systems on the non-negative real line called branching subordinators and closely related to branching L\'evy processes introduced by Bertoin and Mallein arXiv:1703.08078. We pay a particular at
Externí odkaz:
http://arxiv.org/abs/2409.16617
Publikováno v:
Statistics & Probability Letters, Volume 214, 2024, 110192
The discrete-time Hawkes process (DTHP) is a sub-class of $g$-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the
Externí odkaz:
http://arxiv.org/abs/2409.14405
We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the constructio
Externí odkaz:
http://arxiv.org/abs/2409.12515
In the context of irreducible ultracontractive Dirichlet metric measure spaces, we demonstrate the discreteness of the Laplacian spectrum and the corresponding diffusion's irreducibility in connected open sets, without assuming regularity of the boun
Externí odkaz:
http://arxiv.org/abs/2409.07425
On the trace of a discrete-time simple random walk on $\mathbb{Z}^d$ for $d\geq 2$, we consider the evolution of favorite sites, i.e., sites that achieve the maximal local time at a certain time. For $d=2$, we show that almost surely three favorite s
Externí odkaz:
http://arxiv.org/abs/2409.00995
Autor:
Nicolaescu, Liviu I.
For any smooth random Gaussian function $\Phi$ on $\mathbb{R}^m$ we denote by $Z_N(\Phi)$ the number of critical points of $\Phi$ inside the cube $[0,N]^m$. We prove that for certain isotropic random functions $\Phi$ the ratio $N^{-m}Z_N(\Phi)$ conve
Externí odkaz:
http://arxiv.org/abs/2408.14383