mathematics

Kurt Johansson (mathematician)

Kurt Johansson (mathematician) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kurt Johansson (mathematician) rather than just read about it. In short: Kurt Johansson (born 1960) is a Swedish mathematician, specializing in probability theory. Johansson received his PhD in 1988 from Uppsala University under the supervision of Lennart Carleson and is a professor in mathematics at KTH Royal Institute of Technology.

Key takeaways

Kurt Johansson (mathematician) belongs to mathematics; place it in that map before memorising details.
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Connect Kurt Johansson (mathematician) to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Kurt Johansson (mathematician) from memory before moving on to harder problems.

Reference excerpt

Kurt Johansson (born 1960) is a Swedish mathematician, specializing in probability theory. Johansson received his PhD in 1988 from Uppsala University under the supervision of Lennart Carleson and is a professor in mathematics at KTH Royal Institute of Technology. In 2000 Johansson was awarded the Rollo Davidson Prize in Probability theory. In 2002 he was an invited speaker of the International Congress of Mathematicians in Beijing and was awarded the Göran Gustafsson Prize. In 2006 he was elected a member of the Royal Swedish Academy of Sciences. In 2012 he was elected a fellow of the American Mathematical Society.

Selected publications Johansson, Kurt (1997). "On Random Matrices from the Compact Classical Groups". The Annals of Mathematics. 145 (3): 519–545. doi:10.2307/2951843. JSTOR 2951843. Johansson, Kurt (1998). "On fluctuations of eigenvalues of random Hermitian matrices". Duke Mathematical Journal. 91 (1): 151–204. doi:10.1215/S0012-7094-98-09108-6. ISSN 0012-7094. Baik, Jinho; Deift, Percy; Johansson, Kurt (1999). "On the distribution of the length of the longest increasing subsequence of random permutations". Journal of the American Mathematical Society. 12 (4): 1119–1179. doi:10.1090/S0894-0347-99-00307-0. Johansson, Kurt (2000). "Transversal fluctuations for increasing subsequences on the plane". Probability Theory and Related Fields. 116 (4): 445–456. arXiv:math/9910146. doi:10.1007/s004400050258. hdl:2027.42/142448. S2CID 16313314. Johansson, Kurt (2000). "Shape Fluctuations and Random Matrices". Communications in Mathematical Physics. 209 (2): 437–476. arXiv:math/9903134. Bibcode:2000CMaPh.209..437J. doi:10.1007/s002200050027. ISSN 0010-3616. S2CID 16291076. Johansson, Kurt (2001). "Random Growth and Random Matrices". European Congress of Mathematics. Progress in Mathematics, vol. 201. pp. 445–456. doi:10.1007/978-3-0348-8268-2_25. ISBN 978-3-0348-9497-5. Johansson, Kurt (2001). "Discrete orthogonal polynomial ensembles and the Plancherel measure" (PDF). Annals of Mathematics. 153 (1): 259–296. arXiv:math/9906120. doi:10.2307/2661375. JSTOR 2661375. S2CID 14120881. Johansson, Kurt (2002). "Non-intersecting paths, random tilings and random matrices". Probability Theory and Related Fields. 123 (2): 225–280. arXiv:math/0011250. doi:10.1007/s004400100187. S2CID 17994807. Johansson, Kurt (2005). "Non-intersecting, simple, symmetric \- random walks and the extended Hahn kernel". Annales de l'Institut Fourier. 55 (6): 2129–2145. arXiv:math/0409013. doi:10.5802/aif.2155. ISSN 0373-0956. S2CID 8434266. Johansson, K. (2007). "From Gumbel to Tracy-Widom". Probability Theory and Related Fields. 138 (1–2): 75–112. doi:10.1007/s00440-006-0012-7. S2CID 15410267. Adler, Mark; Johansson, Kurt; Van Moerbeke, Pierre (2014). "Double Aztec diamonds and the tacnode process". Advances in Mathematics. 252: 518–571. arXiv:1112.5532. doi:10.1016/j.aim.2013.10.012. Adler, Mark; Chhita, Sunil; Johansson, Kurt; Van Moerbeke, Pierre (2015). "Tacnode GUE-minor processes and double Aztec diamonds" (PDF). Probability Theory and Related Fields. 162 (1–2): 275–325. doi:10.1007/s00440-014-0573-9. S2CID 119126886. Johansson, Kurt (2019). "The two-time distribution in geometric last-passage percolation". Probability Theory and Related Fields. 175 (3–4): 849–895. arXiv:1802.00729. doi:10.1007/s00440-019-00901-9.

References

Worked examples

Example 1 — a first encounter with Kurt Johansson (mathematician)

Start with the simplest possible case. Write down what Kurt Johansson (mathematician) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kurt Johansson (mathematician) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kurt Johansson (mathematician) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kurt Johansson (mathematician)

In research: Kurt Johansson (mathematician) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Kurt Johansson (mathematician) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Kurt Johansson (mathematician) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1960 births, 21st-century Swedish mathematicians, Academic staff of the KTH Royal Institute of Technology, so understanding it makes those chapters shorter.
In everyday life: Look for Kurt Johansson (mathematician) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Kurt Johansson (mathematician) in 20 minutes

Read the reference excerpt below once, without taking notes.
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Work through the three examples above with pen and paper.
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Frequently asked questions

What is Kurt Johansson (mathematician) in simple terms?

Why does Kurt Johansson (mathematician) matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kurt Johansson (mathematician)?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kurt Johansson (mathematician).