| 1. |
- Björnberg, Jakob E., et al.
(författare)
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A Stochastic Model for Virus Growth in a Cell Population
- 2014
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Ingår i: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 51:3, s. 599-612
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Tidskriftsartikel (refereegranskat)abstract
- In this work we introduce a stochastic model for the spread of a virus in a cell population where the virus has two ways of spreading: either by allowing its host cell to live and duplicate, or by multiplying in large numbers within the host cell, causing the host cell to burst and thereby let the virus enter new uninfected cells. The model is a kind of interacting Markov branching process. We focus in particular on the probability that the virus population survives and how this depends on a certain parameter A which quantifies the 'aggressiveness' of the virus. Our main goal is to determine the optimal balance between aggressive growth and long-term success. Our analysis shows that the optimal strategy of the virus (in terms of survival) is obtained when the virus has no effect on the host cell's life cycle, corresponding to lambda = 0. This is in agreement with experimental data about real viruses.
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| 2. |
- Björnberg, Jakob E., 1983, et al.
(författare)
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Characterising random partitions by random colouring
- 2020
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Ingår i: Electronic Communications in Probability. - : Institute of Mathematical Statistics. - 1083-589X. ; 25
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Tidskriftsartikel (refereegranskat)abstract
- Let (X-1, X-2, ...) be a random partition of the unit interval [0, 1], i.e. X-i >= 0 and Sigma(i >= 1) X-i = 1, and let (epsilon(1), epsilon(2), ...) be i.i.d. Bernoulli random variables of parameter p is an element of (0, 1). The Bernoulli convolution of the partition is the random variable Z = Sigma(i >= 1) epsilon X-i(i). The question addressed in this article is: Knowing the distribution of Z for some fixed p is an element of (0, 1), what can we infer about the random partition (X-1, X-2, ...)? We consider random partitions formed by residual allocation and prove that their distributions are fully characterised by their Bernoulli convolution if and only if the parameter p is not equal to 1/2.
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| 3. |
- Björnberg, Jakob E., et al.
(författare)
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Coexistence and noncoexistence of Markovian viruses and their hosts
- 2014
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Ingår i: Journal of Applied Probability. - 0021-9002 .- 1475-6072. ; 51:1, s. 191-208
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Tidskriftsartikel (refereegranskat)abstract
- Examining possibilities for the coexistence of two competing populations is a classic problem which dates back to the earliest 'predator-prey' models. In this paper we study this problem in the context of a model introduced in Bjornberg et al. (2012) for the spread of a virus infection in a population of healthy cells. The infected cells may be seen as a population of 'predators' and the healthy cells as a population of 'prey'. We show that, depending on the parameters defining the model, there may or may not be coexistence of the two populations, and we give precise criteria for this.
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| 4. |
- Björnberg, Jakob E., 1983, et al.
(författare)
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Correlation inequalities for the uniform eight-vertex model and the toric code model
- 2023
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Ingår i: Reviews in Mathematical Physics. - 0129-055X. ; 35:10
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Tidskriftsartikel (refereegranskat)abstract
- We investigate connections between four models in statistical physics and probability theory: (1) the toric code model of Kitaev, (2) the uniform eight-vertex model, (3) random walk on a hypercube, and (4) a classical Ising model with four-body interaction. As a consequence of our analysis (and of the GKS-inequalities for the Ising model) we obtain correlation inequalities for the toric code model and the uniform eight-vertex model.
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| 5. |
- Björnberg, Jakob E., 1983, et al.
(författare)
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Critical parameter of random loop model on trees
- 2018
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Ingår i: Annals of Applied Probability. - : Institute of Mathematical Statistics. - 1050-5164. ; 28:4, s. 2063-2082
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Tidskriftsartikel (refereegranskat)abstract
- We give estimates of the critical parameter for random loop models that are related to quantum spin systems. A special case of the model that we consider is the interchange- or random-stirring process. We consider here the model defined on regular trees of large degrees, which are expected to approximate high spatial dimensions. We find a critical parameter that indeed shares similarity with existing numerical results for the cubic lattice. In the case of the interchange process, our results improve on earlier work by Angel and by Hammond, in that we determine the second-order term of the critical parameter.
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| 6. |
- Björnberg, Jakob E.
(författare)
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Infrared Bound and Mean-Field Behaviour in the Quantum Ising Model
- 2013
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Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 323:1, s. 329-366
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Tidskriftsartikel (refereegranskat)abstract
- We prove an infrared bound for the transverse field Ising model. This bound is stronger than the previously known infrared bound for the model, and allows us to investigate mean-field behaviour. As an application we show that the critical exponent gamma for the susceptibility attains its mean-field value gamma = 1 in dimension at least 4 (positive temperature), respectively 3 (ground state), with logarithmic corrections in the boundary cases.
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| 7. |
- Björnberg, Jakob E., et al.
(författare)
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Recurrence of bipartite planar maps
- 2014
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Ingår i: Electronic Journal of Probability. - 1083-6489. ; 19, s. 31-
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Tidskriftsartikel (refereegranskat)abstract
- This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights and describe it in terms of an infinite mobile. Secondly, we show that the local limit is in all cases almost surely recurrent. And thirdly, we show that for certain choices of weights the local limit has exactly one face of infinite degree and has in that case spectral dimension 4/3 (the latter requires a mild moment condition).
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| 8. |
- Björnberg, Jakob E., 1983, et al.
(författare)
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The interchange process with reversals on the complete graph
- 2019
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Ingår i: Electronic Journal of Probability. - : Institute of Mathematical Statistics. - 1083-6489. ; 24
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Tidskriftsartikel (refereegranskat)abstract
- We consider an extension of the interchange process on the complete graph, in which a fraction of the transpositions are replaced by 'reversals'. The model is motivated by statistical physics, where it plays a role in stochastic representations of xxz-models. We prove convergence to PD(1/2) of the rescaled cycle sizes, above the critical point for the appearance of macroscopic cycles. This extends a result of Schramm on convergence to PD(1) for the usual interchange process.
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| 9. |
- van den Berg, J., et al.
(författare)
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Sharpness versus robustness of the percolation transition in 2d contact processes
- 2015
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Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149 .- 1879-209X. ; 125:2, s. 513-537
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Tidskriftsartikel (refereegranskat)abstract
- We study versions of the contact process with three states, and with infections occurring at a rate depending on the overall infection density. Motivated by a model described in Kefi et al. (2007) for vegetation patterns in arid landscapes, we focus on percolation under invariant measures of such processes. We prove that the percolation transition is sharp (for one of our models this requires a reasonable assumption). This is shown to contradict a form of 'robust critical behaviour' with power law cluster size distribution for a range of parameter values, as suggested in Kefi et al. (2007).
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