Publications
14 results found
Duminil-Copin H, Goswami S, Rodriguez P-F, et al., 2023, EQUALITY OF CRITICAL PARAMETERS FOR PERCOLATION OF GAUSSIAN FREE FIELD LEVEL, DUKE MATHEMATICAL JOURNAL, Vol: 172, Pages: 839-913, ISSN: 0012-7094
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- Citations: 4
Drewitz A, Prevost A, Rodriguez P-F, 2023, Critical exponents for a percolation model on transient graphs, INVENTIONES MATHEMATICAE, Vol: 232, Pages: 229-299, ISSN: 0020-9910
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- Citations: 5
Duminil-Copin H, Rivera A, Rodriguez P-F, et al., 2023, EXISTENCE OF AN UNBOUNDED NODAL HYPERSURFACE FOR SMOOTH GAUSSIAN FIELDS IN DIMENSION <i>d</i> ≥ 3, ANNALS OF PROBABILITY, Vol: 51, Pages: 228-276, ISSN: 0091-1798
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- Citations: 1
Goswami S, Rodriguez P-F, Severo F, 2022, ON THE RADIUS OF GAUSSIAN FREE FIELD EXCURSION CLUSTERS, ANNALS OF PROBABILITY, Vol: 50, Pages: 1675-1724, ISSN: 0091-1798
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- Citations: 6
Drewitz A, Prevost A, Rodriguez P-F, 2022, Cluster capacity functionals and isomorphism theorems for Gaussian free fields, PROBABILITY THEORY AND RELATED FIELDS, Vol: 183, Pages: 255-313, ISSN: 0178-8051
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- Citations: 3
Rodriguez P-F, 2019, On pinned fields, interlacements, and random walk on (Z/NZ)2, Probability Theory and Related Fields, Vol: 173, Pages: 1265-1299, ISSN: 0178-8051
We define two families of Poissonian soups of bidirectional trajectories on Z2, which can be seen to adequately describe the local picture of the trace left by a random walk on the two-dimensional torus (Z/NZ)2, started from the uniform distribution, run up to a time of order (NlogN)2 and forced to avoid a fixed point. The local limit of the latter was recently established in Comets et al. (Commun Math Phys 343:129–164, 2016). Our construction proceeds by considering, somewhat in the spirit of statistical mechanics, a sequence of “finite volume” approximations, consisting of random walks avoiding the origin and killed at spatial scale N, either using Dirichlet boundary conditions, or by means of a suitably adjusted mass. By tuning the intensity u of such walks with N, the occupation field can be seen to have a nontrivial limit, corresponding to that of the actual random walk. Our construction thus yields a two-dimensional analogue of the random interlacements model introduced in Sznitman (Ann Math 171(3):2039–2087, 2010) in the transient case. It also links it to the pinned free field in Z2, by means of a (pinned) Ray–Knight type isomorphism theorem.
Drewitz A, Prévost A, Rodriguez P-F, 2018, The sign clusters of the massless gaussian free field percolate on {Z}^{d}, d⩾ 3 (and more), Communications in Mathematical Physics, Vol: 362, Pages: 513-546, ISSN: 0010-3616
We investigate the percolation phase transition for level sets of the Gaussian free field on Zd, with d⩾3, and prove that the corresponding critical parameter h*(d) is strictly positive for all d⩾3, thus settling an open question from (Rodriguez and Sznitman in Commun Math Phys 320(2):571–601, 2013). In particular, this implies that the sign clusters of the Gaussian free field percolate on Zd, for all d⩾3. Among other things, our construction of an infinite cluster above small, but positive level h involves random interlacements at level u > 0, a random subset of Zd with desirable percolative properties, introduced in Sznitman (Ann Math (2) 171(3):2039–2087, 2010) in a rather different context, a certain Dynkin-type isomorphism theorem relating random interlacements to the Gaussian free field (Sznitman in Electron Commun Probab 17(9):9, 2012), and a recent coupling of these two objects (Lupu in Ann Probab 44(3):2117–2146, 2016), lifted to a continuous metric graph structure over Zd.
Biskup M, Rodriguez P-F, 2018, Limit theory for random walks in degenerate time-dependent random environments, Journal of Functional Analysis, Vol: 274, Pages: 985-1046, ISSN: 0022-1236
Rodriguez P-F, 2017, A 0–1 law for the massive Gaussian free field, Probability Theory and Related Fields, Vol: 169, Pages: 901-930, ISSN: 0178-8051
Fröhlich J, Rodríguez P-F, 2017, On Cluster Properties of Classical Ferromagnets in an External Magnetic Field, Journal of Statistical Physics, Vol: 166, Pages: 828-840, ISSN: 0022-4715
Drewitz A, Rodriguez P-F, 2015, High-dimensional asymptotics for percolation of Gaussian free field level sets, Electronic Journal of Probability, Vol: 20, ISSN: 1083-6489
Rodriguez P-F, 2014, Level set percolation for random interlacements and the Gaussian free field, Stochastic Processes and their Applications, Vol: 124, Pages: 1469-1502, ISSN: 0304-4149
Rodriguez P-F, Sznitman A-S, 2013, Phase Transition and Level-Set Percolation for the Gaussian Free Field, Communications in Mathematical Physics, Vol: 320, Pages: 571-601, ISSN: 0010-3616
Fröhlich J, Rodriguez P-F, 2012, Some applications of the Lee-Yang theorem, Journal of Mathematical Physics, Vol: 53, ISSN: 0022-2488
<jats:p>For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for \documentclass[12pt]{minimal}\begin{document}$\textrm {Re} \ \! h \ne 0$\end{document} Re h≠0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.</jats:p>
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