Global divergence of spatial coalescents (2009)
Angel, Omer, Berestycki, Nathanael, Limic, Vlada
A class of processes called spatial \Lambda-coalescents was recently introduced by Limic and Sturm (2006). In these models particles perform independent random walks on some underlying graph G. In...
VRRW on complete-like graphs: almost sure behavior (2009)
Limic, Vlada, Volkov, Stanislav
By a theorem of Volkov (2001) we know that on most graphs, with positive probability, the linearly vertex-reinforced random walk (VRRW) stays within a finite "trapping" subgraph at all large times....
The $\Lambda$-coalescent speed of coming down from infinity (2008)
Berestycki, Julien, Berestycki, Nathanael, Limic, Vlada
Consider a $\Lambda$-coalescent that comes down from infinity (meaning that it starts from a configuration containing infinitely many blocks at time 0, yet it has a finite number $N_t$ of blocks at...
Coalescent processes arising in a study of diffusive clustering (2007)
Greven, Andreas, Limic, Vlada, Winter, Anita
This paper studies spatial coalescents on $\Z^2$. In our setting, the partition elements are located at the sites of $\Z^2$ and undergo local delayed coalescence and migration. The system starts in...
The spatial Λ-coalescent (2006)
Limic, Vlada; University Of British Columbia; Limic@math.ubc.ca, Sturm, Anja; University Of Delaware; Sturm@math.udel.edu
This paper extends the notion of the Λ-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial Λ-coalescent migrate in a (finite) geographical space...
Attracting edge and strongly edge reinforced walks (2006)
The goal is to show that an edge-reinforced random walk on a graph of bounded degree, with reinforcement weight function $W$ taken from a general class of reciprocally summable reinforcement weight...
The spatial $\Lambda$-coalescent (2005)
This paper extends the notion of the $\la$-coalescent of Pitman (1999) to the spatial setting. The partition elements of the spatial $\Lambda$-coalescent migrate in a (finite) geographical space and...
Greven, Andreas; University Of Erlangen-Nuernberg; Greven@mi.uni-erlangen.de, Limic, Vlada; University Of British Columbia; Limic@math.ubc.ca, Winter, Anita; University Of Erlangen-Nuernberg; Winter@mi.uni-erlangen.de
We consider spatially interacting Moran models and their diffusion limit which are interacting Fisher-Wright diffusions. The Moran model is a spatial population model with individuals of different...
The Beurling Estimate for a Class of Random Walks (2004)
Lawler, Gregory F; Cornell University; Lawler@math.cornell.edu, Limic, Vlada; University Of British Columbia; Limic@math.ubc.ca
An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -&epsilon reaches the unit circle without...
More rigorous results on the Kauffman–Levin model of evolution (2004)
The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts...
The Beurling estimate for a class of random walks (2004)
Lawler, Gregory F., Limic, Vlada
An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -eps reaches the unit circle without...
Rigorous results for the N K model (2003)
Durrett, Richard, Limic, Vlada
Motivated by the problem of the evolution of DNA sequences, Kauffman and Levin introduced a model in which fitnesses were assigned to strings of 0's and 1's of length N based on the values observed...
More rigorous results on the Kauffman-Levin model of evolution (2003)
The purpose of this note is to provide proofs for some facts about the NK model of evolution proposed by Kauffman and Levin. In the case of normally distributed fitness summands, some of these facts...
Attracting edge property for a class of reinforced random walks (2003)
Using martingale techniques and comparison with the generalized Urn scheme, it is shown that the edge reinforced random walk on a graph of bounded degree, with the weight function $W(k) =...
A LIFO queue in heavy traffic (2001)
This paper describes the heavy-traffic behavior of an M/G/1 last-in-first-out preemptive resume queue. An appropriate framework for the analysis is provided by measure-valued processes. In...
On the Behavior of LIFO Preemptive Resume Queues in Heavy Traffic (1999)
Limic, Vlada; Cornell University; Limic@math.cornell.edu
This paper studies heavy traffic behavior of a G/G/1 last-in-first-out (LIFO) preemptive resume queue, by extending the techniques developed in Limic (1999). The queue length process exhibits a...
The Entrance Boundary of the Multiplicative Coalescent (1998)
Aldous, David; University Of California, Berkeley; Aldous@stat.berkeley.edu, Limic, Vlada; University Of California, Berkeley; Aldous@stat.berkeley.edu
The multiplicative coalescent $X(t)$ is a $l^2$-valued Markov process representing coalescence of clusters of mass, where each pair of clusters merges at rate proportional to product of masses. From...
Properties of the multiplicative coalescent /--by Vlada Limic. (1998)
Thesis (Ph. D. in Statistics)--University of California, Berkeley, May 1998.
The Entrance Boundary of the Multiplicative Coalescent (1998)
The multiplicative coalescent X(t) is a l 2 -valued Markov process representing coalescence of clusters of mass, where each pair of clusters merges at rate proportional to product of masses. From...