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作者：Mourrat, Jean-Christophe; Valesin, Daniel
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); University of Groningen
摘要：Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with small average graph distance between vertices, but adding an edge comes at a cost measured according to the geometry of the ambient physical space. In most cases, we identify the order of magnitude of the average graph distance as a function of the parameters...
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作者：Fernholz, E. Robert; Karatzas, Ioannis; Ruf, Johannes
作者单位：Columbia University; University of London; London School Economics & Political Science
摘要：in an equity market consisting of a fixed number d of assets with capitalization weights mu(i) (.), is an observable and a nondecreasing function of time. If this observable of the market is not just nondecreasing but actually grows at a rate bounded away from zero, then strong arbitrage can be constructed relative to the market over sufficiently long time horizons. It has been an open issue for more than ten years, whether such strong outperformance of the market is possible also over arbitra...
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作者：Campi, Luciano; Fischer, Markus
作者单位：University of London; London School Economics & Political Science; University of Padua
摘要：We introduce a simple class of mean-field games with absorbing boundary over a finite time horizon. In the corresponding N-player games, the evolution of players' states is described by a system of weakly interacting Ito equations with absorption on first exit from a bounded open set. Once a player exits, her/his contribution is removed from the empirical measure of the system. Players thus interact through a renormalized empirical measure. In the definition of solution to the mean-field game,...
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作者：Mangoubi, Oren; Smith, Aaron
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Ottawa
摘要：We introduce a Markov chain for sampling from the uniform distribution on a Riemannian manifold M, which we call the geodesic walk. We prove that the mixing time of this walk on any manifold with positive sectional curvature C-x(u, v) bounded both above and below by 0 < m(2) <= C-x(u, v) <= M-2 <( )infinity is O*(M-2/m(2)). In particular, this bound on the mixing time does not depend explicitly on the dimension of the manifold. In the special case that M is the boundary of a convex body, we gi...
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作者：Jacod, Jean; Todorov, Viktor
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Northwestern University
摘要：We derive limit theorems for functionals of local empirical characteristic functions constructed from high-frequency observations of Ito semimartingales contaminated with noise. In a first step, we average locally the data to mitigate the effect of the noise, and then in a second step, we form local empirical characteristic functions from the pre-averaged data. The final statistics are formed by summing the local empirical characteristic exponents over the observation interval. The limit behav...
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作者：Frieze, Alan; Pegden, Wesley
作者单位：Carnegie Mellon University
摘要：In the Diffusion Limited Aggregation (DLA) process on Z(2), or more generally Z(d), particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a fractal with dimension strictly less than d. Very little has been shown rigorously about the process, however. We study an analogous process on the Boolean lattice {0, 1}(n), in which particles take random decreasing walks from (1, ... , 1), and stick at the last vertex before the...
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作者：Loeper, Gregoire
作者单位：Monash University; Monash University
摘要：We consider a model of linear market impact, and address the problem of replicating a contingent claim in this framework. We derive a nonlinear Black-Scholes equation that provides an exact replication strategy. This equation is fully nonlinear and singular, but we show that it is well posed, and we prove existence of smooth solutions for a large class of final payoffs, both for constant and local volatility. To obtain regularity of the solutions, we develop an original method based on Legendr...
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作者：Battiston, Marco; Favaro, Stefano; Roy, Daniel M.; Teh, Yee Whye
作者单位：University of Oxford; University of Turin; University of Toronto; Collegio Carlo Alberto
摘要：We characterize the class of exchangeable feature allocations assigning probability V-n,V-k Pi(l=1 WmlUn-ml)-W-k to a feature allocation of n individuals, displaying k features with counts (m(1), . . . ,m(k)) for these features. Each element of this class is parametrized by a countable matrix V and two sequences U and W of nonnegative weights. Moreover, a consistency condition is imposed to guarantee that the distribution for feature allocations of (n - 1) individuals is recovered from that of...
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作者：Chhita, S.; Ferrari, P. L.; Spohn, H.
作者单位：Durham University; University of Bonn; Technical University of Munich
摘要：For stationary KPZ growth in 1 + 1 dimensions, the height fluctuations are governed by the Baik-Rains distribution. Using the totally asymmetric single step growth model, alias TASEP, we investigate height fluctuations for a general class of spatially homogeneous random initial conditions. We prove that for TASEP there is a one-parameter family of limit distributions, labeled by the diffusion coefficient of the initial conditions. The distributions are defined through a variational formula. We...
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作者：Angel, Omer; Kolesnik, Brett
作者单位：University of British Columbia; University of California System; University of California Berkeley
摘要：For fixed r >= 2, we consider bootstrap percolation with threshold r on the Erdos-Renyi graph G(n,p). We identify a threshold for p above which there is with high probability a set of size r that can infect the entire graph. This improves a result of Feige, Krivelevich and Reichman, which gives bounds for this threshold, up to multiplicative constants. As an application of our results, we obtain an upper bound for the threshold for K-4-percolation on G(n,p), as studied by Balogh, Bollobas and ...
