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pro vyhledávání: '"Severo, Franco"'
Autor:
Severo, Franco
In this note, we give a new and short proof for a theorem of Bodineau stating that the slab percolation threshold $\hat{p}_c$ for the FK-Ising model coincides with the standard percolation critical point $p_c$ in all dimensions $d\geq3$. Both proofs
Externí odkaz:
http://arxiv.org/abs/2312.06831
Autor:
Dembin, Barbara, Severo, Franco
We prove that the supercritical phase of Voronoi percolation on $\mathbb{R}^d$, $d\geq 3$, is well behaved in the sense that for every $p>p_c(d)$ local uniqueness of macroscopic clusters happens with high probability. As a consequence, truncated conn
Externí odkaz:
http://arxiv.org/abs/2311.00555
Autor:
Duminil-Copin, Hugo, Goswami, Subhajit, Rodriguez, Pierre-François, Severo, Franco, Teixeira, Augusto
We consider a percolation model, the vacant set $\mathcal{V}^u$ of random interlacements on $\mathbb{Z}^d$, $d \geq 3$, in the regime of parameters $u>0$ in which it is strongly percolative. By definition, such values of $u$ pinpoint a robust subset
Externí odkaz:
http://arxiv.org/abs/2308.07920
Autor:
Duminil-Copin, Hugo, Goswami, Subhajit, Rodriguez, Pierre-François, Severo, Franco, Teixeira, Augusto
We consider the set of points visited by the random walk on the discrete torus $(\mathbb{Z}/N\mathbb{Z})^d$, for $d \geq 3$, at times of order $uN^d$, for a parameter $u>0$ in the large-$N$ limit. We prove that the vacant set left by the walk undergo
Externí odkaz:
http://arxiv.org/abs/2308.07919
Autor:
Duminil-Copin, Hugo, Goswami, Subhajit, Rodriguez, Pierre-François, Severo, Franco, Teixeira, Augusto
In this article, we consider the interlacement set $\mathcal{I}^u$ at level $u>0$ on $\mathbb{Z}^d$, $d \geq3$, and its finite range version $\mathcal{I}^{u,L}$ for $L >0$, given by the union of the ranges of a Poisson cloud of random walks on $\math
Externí odkaz:
http://arxiv.org/abs/2308.07303
We prove that the set of automorphism invariant Gibbs measures for the $\varphi^4$ model on graphs of polynomial growth has at most two extremal measures at all values of $\beta$. We also give a sufficient condition to ensure that the set of all Gibb
Externí odkaz:
http://arxiv.org/abs/2211.00319
Autor:
Severo, Franco
For a large family of stationary continuous Gaussian fields $f$ on $\mathbb{R}^d$, including the Bargmann-Fock and Cauchy fields, we prove that there exists at most one unbounded connected component in the level set $\{f=\ell\}$ (as well as in the ex
Externí odkaz:
http://arxiv.org/abs/2208.04340
Autor:
Muirhead, Stephen, Severo, Franco
Publikováno v:
Prob. Math. Phys. 5 (2024) 357-412
We study the decay of connectivity of the subcritical excursion sets of a class of strongly correlated Gaussian fields. Our main result shows that, for smooth isotropic Gaussian fields whose covariance kernel $K(x)$ is regularly varying at infinity w
Externí odkaz:
http://arxiv.org/abs/2206.10723
We prove that the set of possible values for the percolation threshold $p_c$ of Cayley graphs has a gap at 1 in the sense that there exists $\varepsilon_0>0$ such that for every Cayley graph $G$ one either has $p_c(G)=1$ or $p_c(G) \leq 1-\varepsilon
Externí odkaz:
http://arxiv.org/abs/2111.00555
We prove that cluster observables of level-sets of the Gaussian free field on the hypercubic lattice $\mathbb{Z}^d$, $d\geq3$, are analytic on the whole off-critical regime $\mathbb{R}\setminus\{h_*\}$. This result concerns in particular the percolat
Externí odkaz:
http://arxiv.org/abs/2108.05294