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Feedback Effects between Similarity and Social Influence in Online Communities
"... A fundamental open question in the analysis of social networks is to understand the interplay between similarity and social ties. People are similar to their neighbors in a social network for two distinct reasons: first, they grow to resemble their current friends due to social influence; and second ..."
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Cited by 162 (8 self)
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A fundamental open question in the analysis of social networks is to understand the interplay between similarity and social ties. People are similar to their neighbors in a social network for two distinct reasons: first, they grow to resemble their current friends due to social influence; and second, they tend to form new links to others who are already like them, a process often termed selection by sociologists. While both factors are present in everyday social processes, they are in tension: social influence can push systems toward uniformity of behavior, while selection can lead to fragmentation. As such, it is important to understand the relative effects of these forces, and this has been a challenge due to the difficulty of isolating and quantifying them in real settings. We develop techniques for identifying and modeling the interactions between social influence and selection, using data from online communities where both social interaction and changes in behavior over time can be measured. We find clear feedback effects between the two factors, with rising similarity between two individuals serving, in aggregate, as an indicator of future interaction — but with similarity then continuing to increase steadily, although at a slower rate, for long periods after initial interactions. We also consider the relative value of similarity and social influence in modeling future behavior. For instance, to predict the activities that an individual is likely to do next, is it more useful to know
RECURRENCE OF EDGEREINFORCED RANDOM WALK ON A Twodimensional Graph
, 2009
"... We consider a linearly edgereinforced random walk on a class of twodimensional graphs with constant initial weights. The graphs are obtained from Z 2 by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edgereinforced random walk on thes ..."
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Cited by 20 (2 self)
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We consider a linearly edgereinforced random walk on a class of twodimensional graphs with constant initial weights. The graphs are obtained from Z 2 by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edgereinforced random walk on these graphs is recurrent. Furthermore, we derive bounds for the probability that the edgereinforced random walk hits the boundary of a large box before returning to its starting point.
Random Dirichlet environment viewed from the particle in dimension d ≥ 3
 ANNALS OF PROBABILITY
, 2013
"... We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z d, RWDE are parameterized by a 2dtuple of positive reals called weights. In this paper ..."
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Cited by 15 (4 self)
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We consider random walks in random Dirichlet environment (RWDE), which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z d, RWDE are parameterized by a 2dtuple of positive reals called weights. In this paper, we characterize for d≥3 the weights for which there exists an absolutely continuous invariant probability distribution for the process viewed from the particle. We can deduce from this result and from [Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 1–8] a complete description of the ballistic regime for d≥3.
Integrability of exit times and ballisticity for random walks in Dirichlet environment
 Electron. J. Probab
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Random walks in random Dirichlet environment are transient in dimension d ≥ 3. Probab. Theory Relat. Fields 151, nos
, 2009
"... Abstract: We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Zd, RWDE are parameterized by a 2duplet of positive reals. We prove that for ..."
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Cited by 15 (5 self)
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Abstract: We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Zd, RWDE are parameterized by a 2duplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension d ≥ 3. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and applies for example to finitely generated transient Cayley graphs. In terms of reinforced random walks it implies that linearly edgeoriented reinforced random walks are transient for d ≥ 3. 1.
Edgereinforced random walk, vertexreinforced jump process and the supersymmetric hyperbolic sigma model
, 2011
"... Edgereinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [5], is a random process that takes values in the vertex set of a graph G, which is more likely to cross edges it has visited before. We show that it can be interpreted as an annealed version of the Vertexreinforce ..."
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Cited by 15 (1 self)
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Edgereinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [5], is a random process that takes values in the vertex set of a graph G, which is more likely to cross edges it has visited before. We show that it can be interpreted as an annealed version of the Vertexreinforced jump process (VRJP), conceived by Werner and first studied by Davis and Volkov [7, 8], a continuoustime process favouring sites with more local time. We calculate, for any finite graph G, the limiting measure of the centred occupation time measure of VRJP, and interpret it as a supersymmetric hyperbolic sigma model in quantum field theory [13]. This enables us to deduce that VRJP is recurrent in any dimension for large reinforcement, using a localisation result of Disertori and Spencer [12].
Volkov: Learning to signal: analysis of a microlevel reinforcement model
, 2008
"... We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1’s play and plays from the set {1, 2}. Both players win if Player 2’s play equals Nature’s play and lose otherwis ..."
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Cited by 14 (2 self)
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We consider the following signaling game. Nature plays first from the set {1, 2}. Player 1 (the Sender) sees this and plays from the set {A, B}. Player 2 (the Receiver) sees only Player 1’s play and plays from the set {1, 2}. Both players win if Player 2’s play equals Nature’s play and lose otherwise. Players are told whether they have won or lost, and the game is repeated. An urn scheme for learning coordination in this game is as follows. Each node of the desicion tree for Players 1 and 2 contains an urn with balls of two colors for the two possible decisions. Players make decisions by drawing from the appropriate urns. After a win, each ball that was drawn is reinforced by adding another of the same color to the urn. A number of equilibria are possible for this game other than the optimal ones. However, we show that the urn scheme achieves asymptotically optimal coordination.
Excited random walks: results, methods, open problems
 Bulletin of the Institute of Mathematics, Academia Sinica (N.S.), special issue in honor of S.R.S. Varadhan’s 70th birthday
"... on the occasion of his 70th birthday. We consider a class of selfinteracting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the ddimensional integer lattice. The main purpose of this paper is twofold: to give a survey of known results and ..."
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on the occasion of his 70th birthday. We consider a class of selfinteracting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the ddimensional integer lattice. The main purpose of this paper is twofold: to give a survey of known results and some of the methods and to present several new results. The latter include functional limit theorems for transient onedimensional excited random walks in bounded i.i.d. cookie environments as well as some zeroone laws. Several open problems are stated. 1. Model Description Random walks (RWs) and their scaling limits are probably the most widely known and frequently used stochastic processes in probability theory, mathematical physics, and applications. Studies of a RW in a random medium are an attempt to understand which macroscopic effects can be seen and modeled by subjecting the RW’s dynamics on a microscopic level to various kinds of noise, for example, allowing it to interact with a random
Growth of preferential attachment random graphs via continuoustime branching processes
 Proc. Indian Acad. Sci. (Math. Sci
, 2008
"... Some growth asymptotics of a version of “preferential attachment ” random graphs are studied through an embedding into a continuoustime branching scheme. These results complement and extend previous work in the literature. ..."
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Cited by 9 (3 self)
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Some growth asymptotics of a version of “preferential attachment ” random graphs are studied through an embedding into a continuoustime branching scheme. These results complement and extend previous work in the literature.