| 2023Marina Ferreira, Eugenia Franco, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Coagulation equations with source leading to anomalous self-similarity
2023
https://arxiv.org/abs/2305.16921
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| 2022Iulia Cristian, Marina A. Ferreira, Eugenia Franco and Juan J. L. Velázquez
Long-time asymptotics for coagulation equations with injection that do not have stationary solutions
2022
https://ui.adsabs.harvard.edu/abs/2022arXiv221116399C
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| Marina A. Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Non-power law constant flux solutions for the Smoluchowski coagulation equation
2022
https://arxiv.org/abs/2207.09518
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| Marina A. Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Asymptotic localization in multicomponent mass conserving coagulation equations
2022
https://arxiv.org/abs/2203.08076
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| 2020D. Betea, P.L. Ferrari and A. Occelli
The half-space Airy stat process
preprint: arXiv:2012.10337 2020
https://arxiv.org/abs/2012.10337
Abstract: We study the multipoint distribution of stationary half-space last passage percolation with exponentially weighted times. We derive both finite-size and asymptotic results for this distribution. In the latter case we observe a new one-parameter process we call half-space Airy stat. It is a one-parameter generalization of the Airy stat process of Baik-Ferrari-Péché, which is recovered far away from the diagonal. All these results extend the one-point results previously proven by the authors. |
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| Ofer Busani and Patrik L. Ferrari
Universality of the geodesic tree in last passage percolation
preprint, arXiv:2008.07844 2020
https://arxiv.org/abs/2008.07844
Abstract: In this paper we consider the geodesic tree in exponential last passage percolation. We show that for a large class of initial conditions around the origin, the line-to-point geodesic that terminates in a cylinder of width $o(N^{2/3})$ and length $o(N)$ agrees in the cylinder, with the stationary geodesic sharing the same end point. In the case of the point-to-point model, we consider width $\delta N^{2/3}$ and length up to $\delta^{3/2} N/(\log(\delta^{-1}))^3$ and provide lower and upper bound for the probability that the geodesics agree in that cylinder. |
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| David Fajman, Gernot Heißel and Jin Woo Jang
Averaging with a time-dependent perturbation parameter
2020
https://ui.adsabs.harvard.edu/abs/2020arXiv200612844F
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| Maximillian Fels and Lisa B. Hartung
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Extremal process in the weakly correlated regime
2020
https://arxiv.org/abs/2002.00925
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| Maximilian Fels and Lisa B. Hartung
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Convergence of the maximum in the regime of weak correlations
2020
https://arxiv.org/abs/1912.13184
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| P.L. Ferrari and B. Vető
Upper tail decay of KPZ models with Brownian initial conditions
preprint,arXiv:2007.13496 2020
https://arxiv.org/abs/2007.13496
Abstract: In this paper we consider the limiting distribution of KPZ growth models with random but not stationary initial conditions introduced in [Chhita-Ferrari-Spohn 2018]. The one-point distribution of the limit is given in terms of a variational problem. By directly studying it, we deduce the right tail asymptotic of the distribution function. This gives a rigorous proof and extends the results obtained in [Meerson-Schmidt 2017]. |
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| P.L. Ferrari, Muhittin Mungan and M. Mert Terzi
The Preisach graph and longest increasing subsequences
arXiv:2004.03138 2020
https://arxiv.org/abs/2004.03138
Abstract: The Preisach graph is a directed graph associated with a permutation ÏâSN. We give an explicit bijection between the vertices and increasing subsequences of Ï, with the property that its length equals the degree of nesting of the vertex inside a hierarchy of cycles and sub-cycles. As a consequence, the nesting degree of the Preisach graph equals the length of the longest increasing subsequence. |
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| 2019D. Betea, P.L. Ferrari and A. Occelli
Stationary half-space last passage percolation
preprint: arXiv:1905.08582 2019
https://arxiv.org/abs/1905.08582
Abstract: In this paper we study stationary last passage percolation (LPP) in half-space geometry. We determine the limiting distribution of the last passage time in a critical window close to the origin. The result is a two-parameter family of distributions: one parameter for the strength of the diagonal bounding the half-space (strength of the source at the origin in the equivalent TASEP language) and the other for the distance of the point of observation from the origin. It should be compared with the one-parameter family giving the BaikâRains distributions for full-space geometry. The result is obtained by using a related integrable model, having Pfaffian structure, together with careful analytic continuation and steepest descent analysis. |
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| Anton Bovier, Saeda Marello, P. L. Ferrari and Elena Pulvirenti
Metastability for the dilute Curie-Weiss model with Glauber dynamics
2019
https://arxiv.org/abs/1912.10699
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| Sergio Conti, Matteo Focardi and Flaviana Iurlano
Existence of strong minimizers for the Griffith static fracture model in dimension two
Ann. Inst. Henri Poincaré C, Anal. Non Linéaire, 36: 455-474 2019
10.1016/j.anihpc.2018.06.003
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| Maximillian Fels
Extremes of the 2d scale-inhomogeneous discrete Gaussian free field: Sub-leading order and tightness
2019
https://arxiv.org/abs/1910.09915v1
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| P.L. Ferrari and A. Occelli
Time-time covariance for last passage percolation with generic initial profile
Math. Phys. Anal. Geom., 22: 1 2019
https://doi.org/10.1007/s11040-018-9300-6
Abstract: We consider time correlation for KPZ growth in 1+1 dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of the exact formula of the covariance for the stationary case obtained in [SIGMA 12 (2016), 074]. Furthermore, we prove the universality of the first order correction when the two observation times are close and provide a rigorous bound of the error term. This result holds also for random initial profiles which are not necessarily stationary. |
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| P.L. Ferrari and B. Vető
Fluctuations of the Arctic curve in the tilings of the Aztec diamond on restricted domains
preprint: arXiv:1909.10840 2019
https://arxiv.org/abs/1909.10840
Abstract: We consider uniform random domino tilings of the restricted Aztec diamond which is obtained by cutting off an upper triangular part of the Aztec diamond by a horizontal line. The restriction line asymptotically touches the arctic circle that is the limit shape of the north polar region in the unrestricted model. We prove that the rescaled boundary of the north polar region in the restricted domain converges to the Airy$_2$ process conditioned to stay below a parabola with explicit continuous statistics and the finite dimensional distribution kernels. The limit is the hard-edge tacnode process which was first discovered in the framework of non-intersecting Brownian bridges. The proof relies on a random walk representation of the correlation kernel of the non-intersecting line ensemble which corresponds to a random tiling. |
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| Patrik L. Ferrari and Peter Nejjar
Statistics of TASEP with three merging characteristics
preprint: arXiv:1910.14083 2019
https://arxiv.org/abs/1910.14083
Abstract: In this paper we consider the totally asymmetric simple exclusion process, with non-random initial condition having three regions of constant densities of particles. From left to right, the densities of the three regions are increasing. Consequently, there are three characteristics which meet, i.e., two shocks merge. We study the particle fluctuations at this merging point and show that they are given by a product of three (properly scaled) GOE Tracy-Widom distribution functions. We work directly in TASEP without relying on the connection to last passage percolation. |
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| Marina Ferreira, Jani Lukkarinen, Alessia Nota and Juan J. L. Velázquez
Stationary non-equilibrium solutions for coagulation systems
arXiv e-prints: arXiv:1909.10608 2019
https://ui.adsabs.harvard.edu/abs/2019arXiv190910608F
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| 2018Antonin Chambolle, Sergio Conti and Gilles A. Francfort
Approximation of a britte fracture energy with the constraint of non-interpenetration
Arch. Ration. Mech. Anal., 228: 867-889 2018
10.1007/s00205-017-1207-z
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