Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Prevost, Alexis"'
We study the volume of the critical clusters for the percolation of the level sets of the Gaussian free field on metric graphs. On $\mathbb{Z}^d$ below the upper-critical dimension $d=6$, we show that the largest such cluster in a box of side length
Externí odkaz:
http://arxiv.org/abs/2412.06772
We investigate the bond percolation model on transient weighted graphs ${G}$ induced by the excursion sets of the Gaussian free field on the corresponding metric graph. Under the sole assumption that its sign clusters do not percolate, we derive an e
Externí odkaz:
http://arxiv.org/abs/2405.17417
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For several of
Externí odkaz:
http://arxiv.org/abs/2403.18787
We investigate the bond percolation model on transient weighted graphs ${G}$ induced by the excursion sets of the Gaussian free field on the corresponding metric graph. We assume that balls in ${G}$ have polynomial volume growth with growth exponent
Externí odkaz:
http://arxiv.org/abs/2312.10030
Autor:
Prévost, Alexis
The study of first passage percolation (FPP) for the random interlacements model has been initiated in arXiv:2112.12096, where it is shown that on $\mathbb{Z}^d$, $d\geq 3$, the FPP distance is comparable to the graph distance with high probability.
Externí odkaz:
http://arxiv.org/abs/2309.03880
Let $X$ be a random walk on the torus of side length $N$ in dimension $d\geq 3$ with uniform starting point, and $t_{\text{cov}}$ be the expected value of its cover time, which is the first time that $X$ has visited every vertex of the torus at least
Externí odkaz:
http://arxiv.org/abs/2309.03192
Publikováno v:
Ann. Appl. Probab. 34(3): 2844-2884 (2024)
The study of Gaussian free field level sets on supercritical Galton-Watson trees has been initiated by Ab\"acherli and Sznitman in Ann. Inst. Henri Poincar\'{e} Probab. Stat., 54(1):173--201, 2018. By means of entirely different tools, we continue th
Externí odkaz:
http://arxiv.org/abs/2208.01033
We present a simple method to produce giant lipid pseudo-vesicles (vesicles with an oily cap on the top), trapped in an agarose gel. The method can be implemented using only a regular micropipette and relies on the formation of a water/oil/water doub
Externí odkaz:
http://arxiv.org/abs/2207.06402
Publikováno v:
Electron. J. Probab. 29: 1-54 (2024)
We study percolative properties of excursion processes and the discrete Gaussian free field (dGFF) in the planar unit disk. We consider discrete excursion clouds, defined using random walks as a two-dimensional version of random interlacements, as we
Externí odkaz:
http://arxiv.org/abs/2205.15289
Autor:
Andres, Sebastian, Prévost, Alexis
Publikováno v:
Ann. Appl. Probab. 34.2, 1846-1895 (2024)
We consider first passage percolation (FPP) with passage times generated by a general class of models with long-range correlations on $\mathbb{Z}^d$, $d\geq 2$, including discrete Gaussian free fields, Ginzburg-Landau $\nabla \phi$ interface models o
Externí odkaz:
http://arxiv.org/abs/2112.12096