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作者：Daskalakis, Constantinos; Dimakis, Alexandros G.; Mossel, Elchanan
作者单位：Massachusetts Institute of Technology (MIT); University of Southern California; University of California System; University of California Berkeley
摘要：We study how the structure of the interaction graph of a game affects the existence of pure Nash equilibria. In particular, for a fixed interaction graph, we are interested in whether there are pure Nash equilibria arising when random utility tables are assigned to the players. We provide conditions for the structure of the graph under which equilibria are likely to exist and complementary conditions which make the existence of equilibria highly unlikely. Our results have immediate implication...
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作者：Olvera-Cravioto, Mariana; Blanchet, Jose; Glynn, Peter
作者单位：Columbia University; Stanford University
摘要：Two of the most popular approximations for the distribution of the steady-state waiting time, W-infinity, of the M/G/1 queue are the so-called heavy-traffic approximation and heavy-tailed asymptotic, respectively. If the traffic intensity, rho, is close to 1 and the processing times have finite variance, the heavy-traffic approximation states that the distribution of W-infinity is roughly exponential at scale O((1 - rho)(-1)), while the heavy tailed asymptotic describes power law decay in the ...
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作者：Anderson, David F.; Ganguly, Arnab; Kurtz, Thomas G.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the time discretization is inversely proportional to some (bounded) power of the norm of the state of th...
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作者：Bhamidi, Shankar; Bresler, Guy; Sly, Allan
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of California System; University of California Berkeley; Microsoft
摘要：A variety of random graph models has been developed in recent years to study a range of problems on networks, driven by the wide availability of data from many social, telecommunication, biochemical and other networks. A key model, extensively used in sociology literature, is the exponential random graph model. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs. Sampling from these distribu...
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作者：Oreshkin, Boris N.; Coates, Mark J.
作者单位：McGill University
摘要：This paper examines the impact of approximation steps that become necessary when particle filters are implemented on resource-constrained platforms. We consider particle filters that perform intermittent approximation, either by subsampling the particles or by generating a parametric approximation. For such algorithms, we derive time-uniform bounds on the weak-sense L-p error and present associated exponential inequalities. We motivate the theoretical analysis by considering the leader node pa...
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作者：Kanoria, Yashodhan; Montanari, Andrea
作者单位：Stanford University; Stanford University
摘要：A voter sits on each vertex of an infinite tree of degree k, and has to decide between two alternative opinions. At each time step, each voter switches to the opinion of the majority of her neighbors. We analyze this majority process when opinions are initialized to independent and identically distributed random variables. In particular, we bound the threshold value of the initial bias such that the process converges to consensus. In order to prove an upper bound, we characterize the process o...
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作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Semimartingale reflecting Brownian motions (SRBMs) are diffusion processes with state space the d-dimensional nonnegative orthant, in the interior of which the processes evolve according to a Brownian motion, and that reflect against the boundary in a specified manner. The data for such a process are a drift vector theta, a nonsingular d x d covariance matrix Sigma, and a d x d reflection matrix R. A standard problem is to determine under what conditions the process is positive recurrent. Nece...
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作者：Collins, Benoit; Nechita, Ion
作者单位：University of Ottawa; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：In this paper, we present applications of the calculus developed in Collins and Nechita [Comm. Math. Phys. 297 (2010) 345-370] and obtain an exact formula for the moments of random quantum channels whose input is a pure state thanks to Gaussianization methods. Our main application is an in-depth study of the random matrix model introduced by Hayden and Winter [Comm. Math. Phys. 284 (2008) 263-280] and used recently by Brandao and Horodecki [Open Syst. Inf. Dyn. 17 (2010) 31-52] and Fukuda and ...
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作者：Ekstrom, Erik; Hobson, David
作者单位：Uppsala University; University of Warwick
摘要：It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes, we show how to construct a time-homogeneous stock price model which reproduces the given option prices.
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作者：Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes' principle. The analysis rests on constructing reflecting Brownian motion with drift in a general open connected domain and studying its stationary distribution. In dimension two we utilize known r...
