Fetching the paper…
Reading the bibliography…
These lecture notes offer a gentle introduction to the two-dimensional Discrete Gaussian Free Field with particular attention paid to the scaling limits of the level sets at heights proportional to the absolute maximum.
1902
Earlier work this paper cites.
1903
Earlier work this paper cites.
S. Sheffield and W. Werner (2010). Conformal Loop Ensembles: The Markovian characterization and the loop-soup construction. Ann. Math
1917
Earlier work this paper cites.
K.L. Chung (1948). On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc
1948
Earlier work this paper cites.
A. Stöhr (1950). Uber einige lineare partielle Differenzengleichungen mit konstanten Koeffizienten III. Math. Nachr
1950
Earlier work this paper cites.
C.S.J.A. Nash-Williams (1959). Random walk and electric currents in networks. Proc. Cambridge Philos. Soc
1959
Earlier work this paper cites.
G. Choquet and J. Deny (1960). Sur l’équation de convolution μ = μ ∗ σ \mu=\mu*\sigma . C.R. Acad. Sci. Paris
1960
Earlier work this paper cites.
J. Deny. (1960). Sur l’équation de convolution μ = μ ∗ σ \mu=\mu*\sigma . Séminaire Brelot-Choquet-Deny. Théorie du potentiel
1960
Earlier work this paper cites.
F. J. Dyson (1962). A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys
1962
Earlier work this paper cites.
D. Slepian (1962). The one-sided barrier problem for Gaussian noise. Bell System Tech. J
1962
Earlier work this paper cites.
R.M. Dudley (1967). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal
1967
Earlier work this paper cites.
K. Symanzik (1969). Euclidean quantum field theory
1969
Earlier work this paper cites.
C.W. Fortuin, P.W. Kasteleyn, J. Ginibre (1971). Correlation inequalities on some partially ordered sets Commun. Math. Phys
1971
Earlier work this paper cites.
S. Orey and S.J. Taylor (1974). How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc.(3)
1974
Earlier work this paper cites.
C. Borell (1975). The Brunn-Minkowski inequality in Gauss space. Invent. Math
1975
Earlier work this paper cites.
H.P. McKean (1975). Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math
1975
Earlier work this paper cites.
B.S. Tsirelson, I.A. Ibragimov and V.N. Sudakov (1976). Norms of Gaussian sample functions. In: Proceedings of the 3rd Japan, USSR Symposium on Probability Theory (Tashkent, 1975)
1975
Earlier work this paper cites.
T.J. Cox (1977). Entrance laws for Markov chains. Ann. Probab
1977
Earlier work this paper cites.
M. Bramson (1978). Maximal displacement of branching Brownian motion. Commun. Pure Appl. Math
1978
Earlier work this paper cites.
T.M. Liggett (1978). Random invariant measures for Markov chains, and independent particle systems. Z. Wahrsch. Verw. Gebiete
1978
Earlier work this paper cites.
L. Russo (1978). A note on percolation. Z. Wahrsch. Verw. Gebiete
1978
Earlier work this paper cites.
P.D. Seymour and D.J.A. Welsh (1978). Percolation probabilities on the square lattice. Ann. Discr. Math
1978
Earlier work this paper cites.
L. Russo (1981). On the critical percolation probabilities. Z. Wahrsch. Verw. Gebiete
1981
Earlier work this paper cites.
Y.G. Sinai (1982). The limit behavior of a one-dimensional random walk in a random environment. Teor. Veroyatnost. i Primenen
1982
Earlier work this paper cites.
M. Bramson (1983). Convergence of solutions of the Kolmogorov equation to traveling waves. Mem. Amer. Math. Soc
1983
Earlier work this paper cites.
R. Durrett and T.M. Liggett (1983). Fixed points of the smoothing transformation. Probab. Theory Rel. Fields
1983
Earlier work this paper cites.
T. Lyons (1983). A simple criterion for transience of a reversible Markov chain. Ann. Probab
1983
Earlier work this paper cites.
P.G. Doyle and J.L. Snell (1984). Random walks and electric networks
1984
Earlier work this paper cites.
E.B. Dynkin (1984). Gaussian and non-Gaussian random fields associated with Markov processes. J. Funct. Anal
1984
Earlier work this paper cites.
J.-P. Kahane (1985). Sur le chaos multiplicatif. Ann. Sci. Math. Québec
1985
Earlier work this paper cites.
T.M. Liggett (1985). Interacting Particle Systems
1985
Earlier work this paper cites.
S. P. Lalley and T. Sellke (1987). A conditional limit theorem for the frontier of a branching Brownian motion. Ann. Probab
1987
Earlier work this paper cites.
M. Talagrand (1987). Regularity of Gaussian processes. Acta Math
1987
Earlier work this paper cites.
B. Derrida and H. Spohn (1988). Polymers on disordered trees, spin glasses, and traveling waves. J. Statist. Phys
1988
Earlier work this paper cites.
R.J. Adler (1990). An introduction to continuity, extrema, and related topics for general Gaussian processes
1990
Earlier work this paper cites.
K. A. Berman and M. H. Konsowa (1990). Random paths and cuts, electrical networks, and reversible Markov chains. SIAM J. Discrete Math
1990
Earlier work this paper cites.
F. M. Dekking and B. Host (1991). Limit distributions for minimal displacement of branching random walks, Probab. Theory Rel. Fields
1991
Earlier work this paper cites.
A. K. Chandra, P. Raghavan, W. L. Ruzzo, R. Smolensky, and P. Tiwari (1996). The electrical resistance of a graph captures its commute and cover times. Comput. Complexity
1996
Earlier work this paper cites.
T. Funaki and H. Spohn (1997). Motion by mean curvature from the Ginzburg-Landau ∇ ϕ \nabla\phi interface model. Commun. Math. Phys
1997
Earlier work this paper cites.
S. Janson (1997). Gaussian Hilbert spaces
1997
Earlier work this paper cites.
A. Naddaf and T. Spencer (1997). On homogenization and scaling limit of some gradient perturbations of a massless free field. Commun. Math. Phys
1997
Earlier work this paper cites.
N. Eisenbaum, H. Kaspi, M.B. Marcus, J. Rosen and Z. Shi (2000). A Ray-Knight theorem for symmetric Markov processes. Ann. Probab
2000
Earlier work this paper cites.
E. Bolthausen, J.-D. Deuschel and G. Giacomin (2001). Entropic repulsion and the maximum of the two-dimensional harmonic crystal. Ann. Probab
2001
Cited alongside, same era.
D. Carpentier and P. Le Doussal (2001). Glass transition of a particle in a random potential, front selection in nonlinear renormalization group, and entropic phenomena in Liouville and sinh-Gordon models, Phys. Rev. E
2001
Cited alongside, same era.
G. Giacomin, S. Olla and H. Spohn (2001). Equilibrium fluctuations for ∇ φ \nabla\varphi interface model. Ann. Probab
2001
Cited alongside, same era.
M. Ledoux (2001). The Concentration of Measure Phenomenon
2001
Cited alongside, same era.
A. Dembo, Y. Peres, J. Rosen, and O. Zeitouni (2004). Cover times for Brownian motion and random walks in two dimensions. Ann. of Math. (2)
2004
Cited alongside, same era.
M. Secci (2014). Random Measures and Independent Particle Systems
2014
Later among the works it cites.
A. Shamov (2014). On Gaussian multiplicative chaos. arXiv:1407.4418
2014
Later among the works it cites.
Y. Abe (2015). Maximum and minimum of local times for two-dimensional random walk. Electron. Commun. Probab
2015
Later among the works it cites.
S. Andres, J.-D. Deuschel, M. Slowik (2015). Invariance principle for the random conductance model in a degenerate ergodic environment, Ann. Probab
2015
Later among the works it cites.
L.-P. Arguin and O. Zindy (2015). Poisson-Dirichlet Statistics for the extremes of the two-dimensional discrete Gaussian Free Field. Electron. J. Probab
2015
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
G. Kozma and E. Schreiber (2004). An asymptotic expansion for the discrete harmonic potential. Electron. J. Probab
2004
Cited alongside, same era.
A. Ruzmaikina and M. Aizenman (2005). Characterization of invariant measures at the leading edge for competing particle systems. Ann. Probab
2005
Cited alongside, same era.
O. Daviaud (2006). Extremes of the discrete two-dimensional Gaussian free field. Ann. Probab
2006
Cited alongside, same era.
G. Grimmett (2006). The Random-Cluster Model
2006
Cited alongside, same era.
R.J. Adler and J.E. Taylor (2007). Random fields and geometry
2007
Cited alongside, same era.
M. Biskup and R. Kotecký (2007). Phase coexistence of gradient Gibbs states
2007
Cited alongside, same era.
S. Sheffield (2007). Gaussian free fields for mathematicians. Probab. Theory Rel. Fields
2007
Cited alongside, same era.
N. Berestycki (2015). Diffusion in planar Liouville quantum gravity. Ann. Inst. Henri Poincaré Probab. Stat
2015
Later among the works it cites.
A. Bovier (2015). From spin glasses to Branching Brownian Motion – and back?. In: M. Biskup, J. Černý, R. Kotecký (eds). Random Walks, Random Fields, and Disordered Systems
2015
Later among the works it cites.
A. Chiarini, A. Cipriani, R.S. Hazra (2015). A note on the extremal process of the supercritical Gaussian Free Field. Electron. Commun. Probab
2015
Later among the works it cites.
T. Madaule (2015). Maximum of a log-correlated Gaussian field. Ann. Inst. H. Poincaré Probab. Statist
2015
Later among the works it cites.
2015
Later among the works it cites.
R. Rhodes and V. Vargas (2015). Liouville Brownian Motion at criticality. Poten. Anal
2015
Later among the works it cites.
E. Subag and O. Zeitouni (2015). Freezing and decorated Poisson point processes. Commun. Math. Phys
2015
Later among the works it cites.
D. Belius and W. Wu (2016). Maximum of the Ginzburg-Landau fields, arXiv:1610.04195
2016
Later among the works it cites.
2016
Later among the works it cites.
M. Biskup and O. Louidor (2016). Extreme local extrema of two-dimensional discrete Gaussian free field. Commun. Math. Phys
2016
Later among the works it cites.
2016
Later among the works it cites.
M. Bramson, J. Ding and O. Zeitouni (2016). Convergence in law of the maximum of the two-dimensional discrete Gaussian free field. Commun. Pure Appl. Math
2016
Later among the works it cites.
A. Chiarini, A. Cipriani, R.S. Hazra (2016). Extremes of the supercritical Gaussian Free Field. ALEA, Lat. Am. J. Probab. Math. Stat
2016
Later among the works it cites.
A. Chiarini, A. Cipriani, R.S. Hazra (2016). Extremes of some Gaussian random interfaces. J. Statist. Phys
2016
Later among the works it cites.
C. Garban, R. Rhodes, and V. Vargas (2016). Liouville Brownian motion. Ann. Probab
2016
Later among the works it cites.
R. Lyons and Y. Peres (2016). Probability on Trees and Networks
2016
Later among the works it cites.
T. Madaule, R. Rhodes and V. Vargas (2016). Glassy phase and freezing of log-correlated Gaussian potentials. Ann. Appl. Probab
2016
Later among the works it cites.
J. Miller and S. Sheffield (2016). Imaginary Geometry I: Interacting SLEs. Probab. Theory Rel. Fields
2016
Later among the works it cites.
J. Miller and S. Sheffield (2016). Imaginary geometry II: reversibility of SLE ( ρ 1 ; ρ 2 ) κ {}_{\kappa}(\rho_{1};\rho_{2}) for κ ∈ ( 0 , 4 ) \kappa\in(0,4) . Ann. Probab
2016
Later among the works it cites.
J. Miller and S. Sheffield (2016). Imaginary geometry III: reversibility of SLE κ
2016
Later among the works it cites.
2016
Later among the works it cites.
V. Tassion (2016). Crossing probabilities for Voronoi percolation. Ann. Probab
2016
Later among the works it cites.
Y. Abe and M. Biskup (2017). In preparation
2017
Closest in time.
2017
Closest in time.
D. Belius and N. Kistler (2017). The subleading order of two dimensional cover times. Probab. Theory Rel. Fields
2017
Closest in time.
2017
Closest in time.
N. Berestycki (2017). An elementary approach to Gaussian multiplicative chaos. Electron. J. Probab
2017
Closest in time.
A. Bovier and L. Hartung (2017). Extended convergence of the extremal process of branching Brownian motion. Ann. Appl. Probab
2017
Closest in time.
J. Ding, R. Roy and O. Zeitouni (2017). Convergence of the centered maximum of log-correlated Gaussian fields. Ann. Probab
2017
Closest in time.
2017
Closest in time.
J. Junnila and E. Saksman (2017). Uniqueness of critical Gaussian chaos. Elect. J. Probab
2017
Closest in time.
Y. Abe (2018). Extremes of local times for simple random walks on symmetric trees. Electron. J. Probab
2018
Closest in time.
M. Biskup and O. Louidor (2018). Full extremal process, cluster law and freezing for two-dimensional discrete Gaussian free field. Adv. Math
2018
Closest in time.
A. Cortines, J. Gold and O. Louidor (2018). Dynamical freezing in a spin glass system with logarithmic correlations. Electron. J. Probab
2018
Closest in time.
2018
Closest in time.
E. Powel (2018). Critical Gaussian chaos: convergence and uniqueness in the derivative normalisation. Electron. J. Probab
2018
Closest in time.