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作者：Foutel-Rodier, Felix; Schertzer, Emmanuel
作者单位：University of Oxford; University of Vienna
摘要：Consider a branching Markov process with values in some general type space. Conditional on survival up to generation N, the genealogy of the extant population defines a random marked metric measure space, where individuals are marked by their type and pairwise distances are measured by the time to the most recent common ancestor. In the present manuscript, we devise a general method of moments to prove convergence of such genealogies in the Gromov-weak topology when N ? 8. Informally, the mome...
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作者：Ganguly, Shirshendu; Hegde, Milind
作者单位：University of California System; University of California Berkeley; Columbia University
摘要：We consider last passage percolation on Z(2) with general weight distributions, which is expected to be a member of the Kardar-Parisi-Zhang (KPZ) universality class. In this model, an oriented path between given endpoints which maximizes the sum of the i.i.d. weight variables associated to its vertices is called a geodesic. Under natural conditions of curvature of the limiting geodesic weight profile and stretched exponential decay of both tails of the point-to-point weight, we use geometric a...
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作者：Rosenzweig, Matthew; Staffilani, Gigliola
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Aggregation equations, such as the parabolic-elliptic Patlak-Keller-Segel model, are known to have an optimal threshold for global existence versus finite-time blow-up. In particular, if the diffusion is absent, then all smooth solutions with finite second moment can exist only locally in time. Nevertheless, one can ask whether global existence can be restored by adding a suitable noise to the equation, so that the dynamics are now stochastic. Inspired by the work of Buckmaster et al. (Int Mat...
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作者：Schonbauer, Philipp
作者单位：Imperial College London
摘要：We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove the existence of densities for a class of singular SPDEs. Both of these results are implemented in the setting of regularity structures. For this we construct renormalized models in situations where some of the driving noises are replaced by deterministic Cameron-Martin functions, and we show Lipschitz continuity of these models with respect to the...
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作者：Andreis, Luisa; Koenig, Wolfgang; Langhammer, Heide; Patterson, Robert I. A.
作者单位：Polytechnic University of Milan; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We study an inhomogeneous sparse random graph, G(N), on [N] = {1, . . . , N} as introduced in a seminal paper by Bollobas et al. (Random Struct Algorithms 31(1):3-122, 2007): vertices have a type (here in a compact metric space S), and edges between different vertices occur randomly and independently over all vertex pairs, with a probability depending on the two vertex types. In the limit N -> infinity, we consider the sparse regime, where the average degree is O (1). We prove a large-deviatio...
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作者：Blanc-Renaudie, Arthur
作者单位：Sorbonne Universite
摘要：We introduce a new stick-breaking construction for inhomogeneous continuum random trees. This new construction allows us to prove the necessary and sufficient condition for compactness conjectured by Aldous et al. (Probab Theory Relat Fields 129(2):182-218, 2004) by comparison with Levy trees. We also compute the fractal dimensions (Minkowski, Packing, Hausdorff).
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作者：Ding, Jian; Wu, Yihong; Xu, Jiaming; Yang, Dana
作者单位：Peking University; Yale University; Duke University; Cornell University
摘要：We study the problem of reconstructing a perfect matching M * hidden in a randomly weighted n xn bipartite graph. The edge set includes every node pair in M * and each of the n(n-1) node pairs not in M * independently with probability d/n. The weight of each edge e is independently drawn from the distributionPif e. M * and fromQif e /. M *. We show that if v dB(P, Q) = 1, where B(P, Q) stands for the Bhattacharyya coefficient, the reconstruction error (average fraction of misclassified edges) ...
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作者：Nadtochiy, Sergey; Shkolnikov, Mykhaylo
作者单位：Illinois Institute of Technology; Princeton University; Princeton University
摘要：We consider the Stefan problem with surface tension, also known as the Stefan-Gibbs-Thomson problem, in an ambient space of arbitrary dimension. Assuming the radial symmetry of the initial data we introduce a novel probabilistic notion of solution, which can accommodate the discontinuities in time (of the radius) of the evolving aggregate. Our main result establishes the global existence of a probabilistic solution satisfying the natural upper bound on the sizes of the discontinuities. Moreove...
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作者：Lacker, Daniel; Ramanan, Kavita; Wu, Ruoyu
作者单位：Columbia University; Brown University; Iowa State University
摘要：Consider a system of homogeneous interacting diffusive particles labeled by the nodes of a unimodular Galton-Watson tree, where the state of each node evolves infinitesimally like a d-dimensional diffusion whose drift coefficient depends on (the histories of) its own state and the states of neighboring nodes, and whose diffusion coefficient depends only on (the history of) its own state. Under suitable regularity assumptions on the coefficients, an autonomous characterization is obtained for t...
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作者：Berestycki, Nathanael; Lis, Marcin; Qian, Wei
作者单位：University of Vienna; Technische Universitat Wien; City University of Hong Kong
摘要：We study the dimer model on subgraphs of the square lattice in which vertices on a prescribed part of the boundary (the free boundary) are possibly unmatched. Each such unmatched vertex is called a monomer and contributes a fixed multiplicative weight z > 0 to the total weight of the configuration. A bijection described by Giuliani et al. (J Stat Phys 163(2):211-238, 2016) relates this model to a standard dimer model but on a non-bipartite graph. The Kasteleyn matrix of this dimer model descri...
